Actual solution starts at 11:01. A lot of rambling and unnecessary talking. I don't know if it's to make the video long or what, but it made the video difficult to watch. I suggest writing a script that's tight, to the point, and moving the ad to a written sceren you flash in the beginning.
@@ZeroSleap Well yeah that's sort of the reason people are here. They want to learn math, not hear this guy's life story about how he was a teacher and that stuff. It's great that he's a teacher and has so much experience, but this isn't the best place to share that.
I'll be retiring from work soon after having worked in Commnuication Engineering Field. I find your step by step teachning method absolutely great which will definitely inspire many of math scholars and help them enjoying mathematics.Thanks a lot for that and keep it up!
One thing I want to add, is that for us in Europe, if there is an unknown in the denominator, we always had to note down that the denominator cannot be zero, so in this case it would be noted that x cannot be 1/2 and -(1/2). It was part of the solution for us , but this could be due to regional differences.
@@Kleermaker1000 "The American doesn't exist" It exists as a concept or avatar in the minds of not-Americans. What exactly it means will tend to vary. One thing almost reliable is less need to conform to Europe, since most Americans escape *from* Europe.
An excellent instructor takes the time to introduce new skills reviewing previously taught material that relates to new material being taught. This teacher is serving the needs of all students by keeping them engaged connecting the new material with the previously taught material---step-by-step. Thanks for making the explanations plain enough to be understood by all of your followers--regardless of their level of understanding.
First you will have to recognize the factors in the denominator: a² - b² = (a-b).(a+b) In this case (2x)² - (1)² = (2x - 1) . (2x + 1) And realize that the numerator can be written as 8x - 4 = 4.(2x-1) Which results in 4.(2x -1) / (2x - 1).(2x+1) = 4 / (2x+1)
It would be so cool if sometime you could do test prep videos related to CLT math, or unrelated, videos for those struggling with dyscalculia which is a learning disability that affects how you process numbers (not logic). Wonderful videos! You are a lifesaver. I was homeschooled but never learned more than arithmetic, and I took some years away to work. Now I'm going into college and have to learn higher math, but I'm terrified of it, and I really appreciate how you break it down and clarify each concept. Kudos and thank you!!
Math ruined my life! I wanted to be an airline pilot. For that, back then in the 70’s we had pretty much first have a BS in engineering. I could barely follow algebra 1, did pretty well in geometry. Advanced algebra was a disaster. I went into physiology. Had to take calculus I & 2 for pre-med. I hired a tutor . The first quit, saying I was “unable to understand math” . The second was a post grad working on a PhD in physics. He came to the same conclusion, but he gave me hope. “ for calculus 1 you will have to use one of these 10 formulas and he listed them. Now we are going to work on the wording of the problems, so you will know which formula to use! So, he would write 20 problems and I had to find which formula I should use, and what number went where in the integral calculation. It was like memorizing a script for a play, or poetry, and then quickly recognize which formula I had to use and I wold get an A! I got A in both calculus 1 & 2 without understanding why or how that formula was the right one. I felt cheated by nature! I breezed through the rest of the courses, advanced biology, Chemistry, biochemistry microbiology, anatomy and others. I passed the MCAT and breezed through medical school and graduated Suma Cum Laude, with the second highest GPA á for my medical school class. Now, at the age of 70, having taught in Ivy league medical school, authored over 50 articles in peer reviewed journals as well of being Editor and associate editor of several well known textbooks besides some authors who were Nobel prize laureates, there is only one thing I was never been able to master: ALGEBRA AND CALCULUS! I remember driving my algebra teachers to near madness or despair. They would write a complicated advanced algebra equation on the board, do the obvious simplifications which I understood. Then he would say, “Now we are stuck, let’s think what we can do: lets multiply by 5”. That drew a complete blank in my reasoning! I would ask “why 5? Why not Planks constant? Why not Newton’s gravitational constant of the universe? “ He would look at me as if I was from another planet. “Watch and you will see”. I did watch and to me there was no logic as to why he had picked “5” to multiply. I waited out of respect till he finished the equation, and he would ask me: “now go you see why I di what I did?” I looked at him and would say, I am more confused now than when you multiplied it by 5” Where did you get 5 from? Are you psychic? Did this number just came to you as a Divine revelation?” I would stay after class & Mr McCartney tried to show me how and why he came with these “spontaneous solutions” I kind of understood how he would chose a random number, but it still did not make sense… That’s when I got a tutor. I squeaked by in his class, but in Calculus, it made absolutely no sense to me. Tutors saved my life and I owe them my achievements in Medicine, being an internationally known expert, and having been invited to conferences all over the world. I am now seriously thinking going back all the way to simple fractions and learn calculus before I die! I speak 4 languages, am a quasi-genius in electronics, I love to read quantum physics until it comes to math. I skip that part! So I still have a dream to be a pilot. I am building a full size cockpit of a Boeing 767, on a Thompson platform using electric actuators. Using geometry I can calculate how much 2 actuator have to go down when I am making a descending turn to the left or right.. That makes sense and the formulas come to me naturally. Including the turning rate or an endless screw to match the opposing actuator pushing upward at a different angle. Lot of trial and errors even using math, but aí manage to get it done. Any advice for an old doctor who sucked at math all his life?
The domain is all x except x = -1/2 AND x = 1/2. Even though the factor (2x-1) was factored out, it was part of the denominator of the original expression.
Thank you for bringing this up, I just got here and I consider the given answer to be wrong due to this. If the constraints are stated (x != 1/2, -1/2) then it's ok.
If you know how to factor the difference of two squares, it is simple. You get (2x+1)(2x-1), and it is obvious which of those is a factor of the numerator.
this video is 4 times longer than it needed to be, and even then it fails to be complete : of course you can only eliminate the common factors 2x-1, with the assumtion that x is not 1/2 !!
@@tmjcbs 4x squared -1 = (2x+1) (2x-1) as a denominator. Even though the (2x-1) cancel out each other in the numerator and denominator, the solution cannot equal zero because it would result in a zero denominator. Hence, you have to solve both (2x+1) and (2x-1) for zero so as to avoid a zero denominator. It is permissible to cancel the terms as long as the solution is not zero. If there is a math teacher out there, I would like her/him to check my reasoning.
Greetings. The answer is 4/(3×+1). The answer is determined as follows. First you factor the numerator (8×-4) to get 4(2×-1). Thereafter, you divide numerator by the denominator after factoring 4 times x raised to the 2 power minus 1 to get (2×-1)(2×+1). (2×-1) in the numerator will cancel (2×-1) in the denominator following which you would be left with 4 in the numerator divided by (2×+1) in the denominator. Answer =4/(2×+1).
Best answer to that fractional expression which will be appreciate by many including myself as it says everything with the least use of wording. Compliment.
Extremely important to be able to simplify any mathematical expression! Must have these procedures committed to memory and down cold...99.9% of tests are timed and one is not going to have all day to putz around on any one problem. Very practical stuff here for sure.
@@IRanOutOfPhrases Just that? Well, if you apply the third binomial formula on 4x² - 1, you get (2x + 1) ⋅ (2x - 1). And (8x - 4) / (2x - 1) cancels out to 4. Therefore, you get 4 / (2x + 1) as a simplified term. But you should mention in the task what you want from me.
If you didn't know how to factor, and you just start plugging in numbers, you would see that the numerator is always 4 and the denominator is 2x + 1. ie. plug in 1 and you get 4/3, plug in 2 and you get 4/5, plug in 3 and you get 4/7, plug in 4 and you get 4/9 ,etc.
I'm an engineer and I can honestly say that I haven't done any factoring in a looooong time. I did get the 80's Mohawk though. Appropriate because I took algebra 1 in 1985. I'm watching your videos to help me remember so I can help with my grandkids. Thanks.
(8x - 4) / (4x^2 - 1) 4(2x - 1 )/ (2x - 1)(2x + 1) 4/(2x + 1) If you can't write this down at sight, then the problem is too hard for you, do something easier. You are not meant to have to think much in doing these examples.
I graduated high school 1979 97th percentile in the nation in math. Over the years, I've become incredibly stupid so this is helping me sharpen my skills and I must be getting it back, cuz I did the problem in my head in about 20 seconds.
There certainly are a bunch of petty complaints and comments herein. I wonder why as this guy is good. Solving math is resolving an equation or reducing to the simplist form.
Before I watch your video .. 8x - 4 divided by 4x^2 - 1 Let's see if we can get x to the same value. LONG PAUSE .... Yes we can .. 2x 8x - 4 becomes 4(2x - 1) and 4x^2 - 1 becomes (2x - 1)(2x + 1) so it's 4(2x - 1) divided by (2x - 1)(2x + 1) and now the (2x - 1) 'top and bottom' of the division can just go, leaving us with .. 4 divided by (2x + 1) ... and I think that's it !
Algebra is not a single semester or even a single year. In the US, the current GED "Reasoning Through Mathematics" test can be passed without being able to evaluate algebraic problems as such (but it definitely helps). What amazed me was the emphasis on FOIL (multiplying a binomial by another binomial) that made it a truly make-or-break issue in the test. It would be correct to say "If you don't know how to work with mathematical expressions, including adding, subtracting, multiplication, and division your prospects for a passing score are dim." I think it would be more useful, even popular, to show how problems can be taken from a "real world [he he] example" to a solution. This format has been worn out.
If you know the so-called third quadratic rule, you could do this in your head with some concentration. If not you will need some more thinking and papr work , but undertstanding factoring, you still would figure it out, at least if the school has not dislearned you from using logical thinking, which the schools for the masses do with purpose to hinder ordinary people from social climbing.
Factoring is unnecessary if there is an equation I can use, like the quadratic equation. Teachers often will show the problematic way to solve a problem before showing the simple way. Remember the most important thing is to get to the correct answer in the fewest number of steps.
Caution: When cancelling factors in the numerator and denominator, one can lose information about the function or problem at hand. For example, if the original problem represented a function then by cancelling the 2x -1 term in the numerator and denominator, one loses the information that the original function is not defined at x=1/2. Be careful cancelling terms with x.
@@lamper2 If you put in x = 1/2 in the original formula, you get 0/0. In math, this is an undefined value. Whereas in the 'simplified form', you can put in x = 1/2 just fine and you will get 2 as answer. This is NOT the same, so this shows by 'simplifying' like this, you basically changed the formula. Moral of the story: factoring skills are nice, but beware what you are doing.
@@erwinmulder1338 New York Math Regents asked factoring, multiplying, and dividing fractions, and specified x cannot equal certain numbers so the deominators can't be 0. That is actually a hint. For example, if x cannot equal 3, either x-3 or a multiple of it like 2x-6 is a factor of the denominator.
I left school nearly 60 years ago, and have never in my working life been given an algebra problem to solve, to make something work properly. This seems to me to be math for the sake of it, with no practical application. Am I wrong?
I do like your videos at end I am close to catching on. I am looking for certain approaches to the equation like a like a directory of a search engine in computers and programming you call that bool low wattage serge lines that turn on and off in sequence of patterns formed in rows how do I know all that oh ya I read it, I looking for algorithms like that law falls under squares write out table use your forty-five degrees and count in have visual only in my head we do up and back down to 25, 16, 9, 4,2, One ×itself is one your deminson box all ones square begin, the power of 2 second deminsion that where the law now I just got lost again but that is one I trying to like to algorithm to do algebra. That you for the Bush up it really appreciated Alan Jr Hurdle
I saw what you did, I sort of get what you did, but I regret to say that I didn't understand algebra 55 years ago, and it is still a foreign language to me, making no sense. When I first saw the math problem, I thought the top line was 8 times -4. Obviously my mind refuses to see algebraic equations. I am algebraically dyslectic.
Fun fact: in 5th grade i really struggle to this day to do multiplication and spelling and almost failed 6th and 7th grade but 8th grade I really stepped up my game and tried harder being I need these skills to understand things future wise so im trying to learn the most i can even though im not a fan or studying im making notes
Hi I used to be an A+ student and algebra looks really easy and I have taken algebra 2. I got a b at first but then I got an f because here's what happened. I was home schooled and my parents just put me in a room to do my homework but I found the answer books and basically skipped 8th and 9th grade. Now I want to be a mechanical engineer but I have no foundation. What do I do?
But be aware of the many many errors you will get for these reasonable prices. In many, many of his videos he makes errors and teach the wrong things. See also my comment on this video. Even the demo on his commercial website contains errors!
Would it be correct to say that with 4/2x+1 nothing can be done with the 4 and the 2, such as reducing it to 2 and 1, because the 2 is actually wrapped up with a quantity x and that product + 5 so it's not really 4?
And, at the risk of being..."That Guy".... I'll continue with pointing out that, if we were to graph this expression, there would be removable discontinuity at x equals plus or minus 1/2. And, in fairness to you, the problem was only simplifying, factoring, and nothing more..
Ok, Sounds like you’re the one to ask my question then. Haha! I don’t NEED to know or anything, but now I’m bothered because I haven’t figured it out… 😄 and I just need to figure it out, ok?! 😅 Aaaaanyways. So, say I have a mixed packet of Sweet Bell pepper seeds that contains equal parts of 5 different varieties. What is the minimum number of seeds that I would need to plant in order to ‘guarantee’ that I’ve planted one of each variety. 80% of them + 1, right? Well, what if I had a bucket of seeds?! That’s just a ridiculous amount of Bell peppers. So, instead, I decided that I was willing to utilize two rows in my seed starting tray. That’s 12 cells. There are 39 seeds in the packet. An equal 20%of each variety (orange, white, purple, yellow, and red) included in the packet, according to Burpee. What are the “odds”, “%chance”, or “probability” (i’ve been thinking about this too long and I’m not even sure which I’m asking for anymore. lol) that I will have planted at least one of each variety? Please and thank you
Sorry, but I am so trouble by the way - after so many digressions - you are giving your solving : 4/(2x+1) and 100% to the students providing it. I am 73, but I clearly remember my math teacher : "you only gave half of the solution! You forgot to provide the restriction : IF X NOT EQUAL TO 1/2” Dividing numerator and denominator by 2x-1 is only possible with such restriction!
Good info for passing academic testing, but of little use in the real world for 86% of today's jobs. Not everyone becomes an engineer, scientist, or math teacher. I achieved a 98 on the NY Regents Algebra test and never used this math in 30 years. I have a calculator.
Actual solution starts at 11:01. A lot of rambling and unnecessary talking. I don't know if it's to make the video long or what, but it made the video difficult to watch. I suggest writing a script that's tight, to the point, and moving the ad to a written sceren you flash in the beginning.
Thanks
Zoomer ADHD detected.No communication needed,fast information only.
@@ZeroSleap Well yeah that's sort of the reason people are here. They want to learn math, not hear this guy's life story about how he was a teacher and that stuff. It's great that he's a teacher and has so much experience, but this isn't the best place to share that.
@@ZeroSleap -👴
And even then i land on the TH-cam ads. I already watched some before he started his interminable smug rambling and preening and begging for money.
Thank you for the related examples. You never skip a step and we gain from your proper step by step teaching.
I'll be retiring from work soon after having worked in Commnuication Engineering Field. I find your step by step teachning method absolutely great which will definitely inspire many of math scholars and help them enjoying mathematics.Thanks a lot for that and keep it up!
One thing I want to add, is that for us in Europe, if there is an unknown in the denominator, we always had to note down that the denominator cannot be zero, so in this case it would be noted that x cannot be 1/2 and -(1/2). It was part of the solution for us , but this could be due to regional differences.
Math is not regional but UNIVERSAL.
Of course the "Americlans" always beg to differ.
By the way these videos are unwatchable. I wonder why?!
🤔👎
@@panagdimi "the Americlans always beg to differ."
No begging needed. Americans are different.
@@thomasmaughan4798 They differ much from each other. The American doesn't exist. :)
True, in The Netherlands we have to do that too, and it is logic and correct.
@@Kleermaker1000 "The American doesn't exist"
It exists as a concept or avatar in the minds of not-Americans. What exactly it means will tend to vary. One thing almost reliable is less need to conform to Europe, since most Americans escape *from* Europe.
Thank you. The maths is sound, but I do find so much extraneous chatter to be a distraction. I'm sure it must work for many though.
9:51 - 13:09 problem solving begins / ends.
Thank you!! He talks too much!!!!!
Hint, skip to 9:51, then mute sound and play in double speed...
An excellent instructor takes the time to introduce new skills reviewing previously taught material that relates to new material being taught. This teacher is serving the needs of all students by keeping them engaged connecting the new material with the previously taught material---step-by-step. Thanks for making the explanations plain enough to be understood by all of your followers--regardless of their level of understanding.
First you will have to recognize the factors in the denominator: a² - b² = (a-b).(a+b)
In this case (2x)² - (1)² = (2x - 1) . (2x + 1)
And realize that the numerator can be written as 8x - 4 = 4.(2x-1)
Which results in 4.(2x -1) / (2x - 1).(2x+1) = 4 / (2x+1)
It would be so cool if sometime you could do test prep videos related to CLT math, or unrelated, videos for those struggling with dyscalculia which is a learning disability that affects how you process numbers (not logic).
Wonderful videos! You are a lifesaver. I was homeschooled but never learned more than arithmetic, and I took some years away to work. Now I'm going into college and have to learn higher math, but I'm terrified of it, and I really appreciate how you break it down and clarify each concept. Kudos and thank you!!
Math ruined my life! I wanted to be an airline pilot. For that, back then in the 70’s we had pretty much first have a BS in engineering. I could barely follow algebra 1, did pretty well in geometry. Advanced algebra was a disaster. I went into physiology. Had to take calculus I & 2 for pre-med. I hired a tutor . The first quit, saying I was “unable to understand math” . The second was a post grad working on a PhD in physics. He came to the same conclusion, but he gave me hope. “ for calculus 1 you will have to use one of these 10 formulas and he listed them. Now we are going to work on the wording of the problems, so you will know which formula to use! So, he would write 20 problems and I had to find which formula I should use, and what number went where in the integral calculation. It was like memorizing a script for a play, or poetry, and then quickly recognize which formula I had to use and I wold get an A! I got A in both calculus 1 & 2 without understanding why or how that formula was the right one. I felt cheated by nature! I breezed through the rest of the courses, advanced biology, Chemistry, biochemistry microbiology, anatomy and others.
I passed the MCAT and breezed through medical school and graduated Suma Cum Laude, with the second highest GPA á for my medical school class. Now, at the age of 70, having taught in Ivy league medical school, authored over 50 articles in peer reviewed journals as well of being Editor and associate editor of several well known textbooks besides some authors who were Nobel prize laureates, there is only one thing I was never been able to master: ALGEBRA AND CALCULUS! I remember driving my algebra teachers to near madness or despair. They would write a complicated advanced algebra equation on the board, do the obvious simplifications which I understood. Then he would say, “Now we are stuck, let’s think what we can do: lets multiply by 5”. That drew a complete blank in my reasoning! I would ask “why 5? Why not Planks constant? Why not Newton’s gravitational constant of the universe? “ He would look at me as if I was from another planet. “Watch and you will see”. I did watch and to me there was no logic as to why he had picked “5” to multiply. I waited out of respect till he finished the equation, and he would ask me: “now go you see why I di what I did?” I looked at him and would say, I am more confused now than when you multiplied it by 5” Where did you get 5 from? Are you psychic? Did this number just came to you as a Divine revelation?” I would stay after class & Mr McCartney tried to show me how and why he came with these “spontaneous solutions” I kind of understood how he would chose a random number, but it still did not make sense… That’s when I got a tutor. I squeaked by in his class, but in Calculus, it made absolutely no sense to me. Tutors saved my life and I owe them my achievements in Medicine, being an internationally known expert, and having been invited to conferences all over the world. I am now seriously thinking going back all the way to simple fractions and learn calculus before I die!
I speak 4 languages, am a quasi-genius in electronics, I love to read quantum physics until it comes to math. I skip that part!
So I still have a dream to be a pilot. I am building a full size cockpit of a Boeing 767, on a Thompson platform using electric actuators. Using geometry I can calculate how much 2 actuator have to go down when I am making a descending turn to the left or right..
That makes sense and the formulas come to me naturally. Including the turning rate or an endless screw to match the opposing actuator pushing upward at a different angle. Lot of trial and errors even using math, but aí manage to get it done.
Any advice for an old doctor who sucked at math all his life?
thats a great story. I would guess your continued patience will keep you afloat.
@@tonytor5346
The domain is all x except x = -1/2 AND x = 1/2. Even though the factor (2x-1) was factored out, it was part of the denominator of the original expression.
Thank you for bringing this up, I just got here and I consider the given answer to be wrong due to this. If the constraints are stated (x != 1/2, -1/2) then it's ok.
If you know how to factor the difference of two squares, it is simple. You get (2x+1)(2x-1), and it is obvious which of those is a factor of the numerator.
If you don't know how to factor the difference of two squares, then it is impossible.
this video is 4 times longer than it needed to be, and even then it fails to be complete : of course you can only eliminate the common factors 2x-1, with the assumtion that x is not 1/2 !!
I am no expert in math, but I believe it is with the assumption that x is not 1/2 nor -1/2.
@@MFM230 I see that assumption nowhere explicitly...
@@tmjcbs 4x squared -1 = (2x+1) (2x-1) as a denominator. Even though the (2x-1) cancel out each other in the numerator and denominator, the solution cannot equal zero because it would result in a zero denominator. Hence, you have to solve both (2x+1) and (2x-1) for zero so as to avoid a zero denominator. It is permissible to cancel the terms as long as the solution is not zero. If there is a math teacher out there, I would like her/him to check my reasoning.
@@MFM230 I happen to be a math teacher, your reasoning is right. I can only repeat my earlier comment: in the video that assumption is made nowhere...
@@tmjcbs Thanks for checking my math.
Greetings. The answer is 4/(3×+1). The answer is determined as follows. First you factor the numerator (8×-4) to get 4(2×-1). Thereafter, you divide numerator by the denominator after factoring 4 times x raised to the 2 power minus 1 to get (2×-1)(2×+1). (2×-1) in the numerator will cancel (2×-1) in the denominator following which you would be left with 4 in the numerator divided by (2×+1) in the denominator. Answer =4/(2×+1).
I think after you say, "Greetings," you meant to say, "The answer is 4/2x=1" not 4/3x=1.
@@bowlinghuddles17 Greetings. Correct. Thanks for your attentiveness. Blessings.
Thank You 👍
Best answer to that fractional expression which will be appreciate by many including myself as it says everything with the least use of wording.
Compliment.
Extremely important to be able to simplify any mathematical expression! Must have these procedures committed to memory and down cold...99.9% of tests are timed and one is not going to have all day to putz around on any one problem. Very practical stuff here for sure.
I'm an engineer and I've been reviewing this material lately. Math is amazing. Good video. Keep it up.
But be aware of the many errors, see my comment.
Great speech to the kids. Thanks for understanding
I always found that maths teachers were not good teachers. Just enjoyed doing fast maths and showing off how clever they are.
You mix teaching algebra with history and practical advice so well 👏 👌
And with errors, again and again
Your digression is always too much, makes me lose interest in the main thing. Learn to be direct and face what you have set out to do.
True.
FYI - it's "lose interest". "Loose" rhymes with "goose", "moose", and "noose". "Lose" rhymes with "shoes."
@@laurendoe168 all of them rhyme
I'm totally in disagreement. His explanation is great 👍
@@pittyconor2489 yes, that's my point. "Loose" does not rhyme with "shoes". "Loose" means "not tight". "Lose" means "unable to locate"
Depends on the value of x.
If x = 1, then (8x - 4) / (4x² - 1) = 4/3
If x = 0, then (8x - 4) / (4x² - 1) = 4 etc.
The challenge is to simplify. Not input values for x to see what it produces
@@IRanOutOfPhrases Just that? Well, if you apply the third binomial formula on 4x² - 1, you get (2x + 1) ⋅ (2x - 1).
And (8x - 4) / (2x - 1) cancels out to 4. Therefore, you get 4 / (2x + 1) as a simplified term.
But you should mention in the task what you want from me.
@@Nikioko He does that at the 0:17 mark
4(2x-1)/(2×-1)(2×+1)=4/(2x+1)
If you didn't know how to factor, and you just start plugging in numbers, you would see that the numerator is always 4 and the denominator is 2x + 1. ie. plug in 1 and you get 4/3, plug in 2 and you get 4/5, plug in 3 and you get 4/7, plug in 4 and you get 4/9 ,etc.
The task is to *simplify* not to solve for X. Since it is not an equation, there cannot be a solution for x.
I'm an engineer and I can honestly say that I haven't done any factoring in a looooong time. I did get the 80's Mohawk though. Appropriate because I took algebra 1 in 1985. I'm watching your videos to help me remember so I can help with my grandkids. Thanks.
thanks for the factoring emphasis, truly tough to see easily. Must practice that one.
Thanks for the refresher…. I’m having a ton of fun with your videos
Thanks for sharing ……..you make it look so easy Man !
Too much talking !!
Dats what he supposed to do
Always
I disagree
(8x - 4) / (4x^2 - 1)
4(2x - 1 )/ (2x - 1)(2x + 1)
4/(2x + 1)
If you can't write this down at sight, then the problem is too hard for you, do something easier. You are not meant to have to think much in doing these examples.
How are you distinguishing between an X and a multiplication sign? You seem to be writing a multiplication sign.
What does it equal, it has to equal something to solve it, you can’t assume it equals zero. If you just simplify as you suggest you get 4/(2x + 1).
exactly. it wasn't asked to be solved it was just asked to be simplified.
Math is the purest, most powerful science of all. Go Math! :-)
The fact that this comment is from someone with your username is nice hehe
You’re an excellent teacher, John! Thank you!
Breaking this down we 4(2x-1) on the top and (2x+1)(2x-1) in the bottom canceling the (2x-1) leaves 4 over 2x+1
You really need to put the point of the exercise in your title. "100% must know to pass" is not helpful statement in the opening screen.
😂Your teaching technic is brilliant. I love your sense of humor.
I cant believe someone moans about digression ..your a good tutor .....unbelievable
You are absolutely correct Devon wilson
I graduated high school 1979 97th percentile in the nation in math.
Over the years, I've become incredibly stupid so this is helping me sharpen my skills and I must be getting it back, cuz I did the problem in my head in about 20 seconds.
Skip to 10:54
Thank you!!!
I'm from Sierra Leone, how am i getting your link
There certainly are a bunch of petty complaints and comments herein. I wonder why as this guy is good. Solving math is resolving an equation or reducing to the simplist form.
That's your point. The complaints are not petty. They come from intelligent maths students. Why is your backside burning
You can simplify it as long as 2x-1 is not equal to zero
My teacher in grade 6 doesnt teach us and let the top 1 student teach us. So ur vids help me very much
Before I watch your video ..
8x - 4 divided by 4x^2 - 1
Let's see if we can get x to the same value.
LONG PAUSE .... Yes we can .. 2x
8x - 4 becomes 4(2x - 1) and 4x^2 - 1 becomes (2x - 1)(2x + 1)
so it's 4(2x - 1) divided by (2x - 1)(2x + 1)
and now the (2x - 1) 'top and bottom' of the division can just go, leaving us with ..
4 divided by (2x + 1) ... and I think that's it !
Algebra is not a single semester or even a single year. In the US, the current GED "Reasoning Through Mathematics" test can be passed without being able to evaluate algebraic problems as such (but it definitely helps). What amazed me was the emphasis on FOIL (multiplying a binomial by another binomial) that made it a truly make-or-break issue in the test.
It would be correct to say "If you don't know how to work with mathematical expressions, including adding, subtracting, multiplication, and division your prospects for a passing score are dim."
I think it would be more useful, even popular, to show how problems can be taken from a "real world [he he] example" to a solution. This format has been worn out.
Will you have a video on Ordinary and Partial Differential Equations, and Linear Algebra?
If you know the so-called third quadratic rule, you could do this in your head with some concentration. If not you will need some more thinking and papr work , but undertstanding factoring, you still would figure it out, at least if the school has not dislearned you from using logical thinking, which the schools for the masses do with purpose to hinder ordinary people from social climbing.
Factoring is unnecessary if there is an equation I can use, like the quadratic equation. Teachers often will show the problematic way to solve a problem before showing the simple way. Remember the most important thing is to get to the correct answer in the fewest number of steps.
Caution: When cancelling factors in the numerator and denominator, one can lose information about the function or problem at hand. For example, if the original problem represented a function then by cancelling the 2x -1 term in the numerator and denominator, one loses the information that the original function is not defined at x=1/2. Be careful cancelling terms with x.
Thanx. I wish He wouldn't have glossed over the "almost " conclusion. Oh well, buy the book etc.
HUH?
@@lamper2 If you put in x = 1/2 in the original formula, you get 0/0. In math, this is an undefined value. Whereas in the 'simplified form', you can put in x = 1/2 just fine and you will get 2 as answer. This is NOT the same, so this shows by 'simplifying' like this, you basically changed the formula. Moral of the story: factoring skills are nice, but beware what you are doing.
@@erwinmulder1338
There's another restriction as well. If x=-1/2, the expression becomes -8/0, which is also undefined.
@@erwinmulder1338 New York Math Regents asked factoring, multiplying, and dividing fractions, and specified x cannot equal certain numbers so the deominators can't be 0. That is actually a hint. For example, if x cannot equal 3, either x-3 or a multiple of it like 2x-6 is a factor of the denominator.
If it takes a hen and a half, a day and a half, to lay an egg and a half, how long will it take one hen to lay a dozen eggs?
4x^2-1~>8x-1
I left school nearly 60 years ago, and have never in my working life been given an algebra problem to solve, to make something work properly. This seems to me to be math for the sake of it, with no practical application. Am I wrong?
Love your videos! Im retired now and do this stuff for fun :)
I do like your videos at end I am close to catching on. I am looking for certain approaches to the equation like a like a directory of a search engine in computers and programming you call that bool low wattage serge lines that turn on and off in sequence of patterns formed in rows how do I know all that oh ya I read it, I looking for algorithms like that law falls under squares write out table use your forty-five degrees and count in have visual only in my head we do up and back down to 25, 16, 9, 4,2,
One ×itself is one your deminson box all ones square begin, the power of 2 second deminsion that where the law now I just got lost again but that is one I trying to like to algorithm to do algebra. That you for the Bush up it really appreciated Alan Jr Hurdle
Algebra two final is tomorrow
Thanks for the help
I saw what you did, I sort of get what you did, but I regret to say that I didn't understand algebra 55 years ago, and it is still a foreign language to me, making no sense. When I first saw the math problem, I thought the top line was 8 times -4. Obviously my mind refuses to see algebraic equations. I am algebraically dyslectic.
When did maths become singular ?
We say "math" in North America and they say "maths" in the U.K. but they both refer to "mathematics".
Could you have said... 2/(x + ½) ?
yes... but fractions within a fraction are typically avoided
“ A crummy commercial!”
- - Ralphie, A Christmas Story!
😂😂😂
this one looks like a trick 4(2x-1)/{(2x +1)(2x-1)}= 4/(2x+1) so i was there about 12.44 i have physical chemistry books available....
Fun fact: in 5th grade i really struggle to this day to do multiplication and spelling and almost failed 6th and 7th grade but 8th grade I really stepped up my game and tried harder being I need these skills to understand things future wise so im trying to learn the most i can even though im not a fan or studying im making notes
Hi I used to be an A+ student and algebra looks really easy and I have taken algebra 2. I got a b at first but then I got an f because here's what happened. I was home schooled and my parents just put me in a room to do my homework but I found the answer books and basically skipped 8th and 9th grade. Now I want to be a mechanical engineer but I have no foundation. What do I do?
I'd recommend taking remedial classes to catch up or finding a tutor who can catch you up.
4/(2x+1)
I got it. But I wasn't sure I was done until I watched the video.
Very reasonable prices for courses and notes!
But be aware of the many many errors you will get for these reasonable prices. In many, many of his videos he makes errors and teach the wrong things.
See also my comment on this video. Even the demo on his commercial website contains errors!
Great teaching method for students.
Those who think that they are better and find only faults in this teaching method, create your own video.😂 ✌️
4/2X+1
4?
Would it be correct to say that with 4/2x+1 nothing can be done with the 4 and the 2, such as reducing it to 2 and 1, because the 2 is actually wrapped up with a quantity x and that product + 5 so it's not really 4?
Get to it and stop the fluff! I’m trying to learn!
you keep saying that you are a high school math teacher but from where ?
4 over 2x+1
And, at the risk of being..."That Guy".... I'll continue with pointing out that, if we were to graph this expression, there would be removable discontinuity at x equals plus or minus 1/2. And, in fairness to you, the problem was only simplifying, factoring, and nothing more..
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YOU all ready lost me. I see it when you write it out. and can follow that, but had not set in the sequence you did if on my own
I don't remember this type of problem in my algebra classes. I graduated high school in 1997
Very good video 👌
4/2x+ 1
How many topics in algebra do your notes cover?
x≠±(1/2)
hmmm i guess ive forgotten how to do higher level factoring
You don't want to belabor the point. Is that what you mean? I'm going to watch your factoring videos right now.
X != 1/2 and x ! = -1/2
4/(2x+1). 14 seconds. In my head.
i aint good at math and i could never simplify no fractions, I never understood it and I am trying my hardest I still cant understand it
Damn! Couldn't work it...
Back to the drawing board.
This is grade 3 maths in China brah, they some hard core maths ppl
Ok, Sounds like you’re the one to ask my question then. Haha! I don’t NEED to know or anything, but now I’m bothered because I haven’t figured it out… 😄 and I just need to figure it out, ok?! 😅
Aaaaanyways. So, say I have a mixed packet of Sweet Bell pepper seeds that contains equal parts of 5 different varieties. What is the minimum number of seeds that I would need to plant in order to ‘guarantee’ that I’ve planted one of each variety. 80% of them + 1, right? Well, what if I had a bucket of seeds?! That’s just a ridiculous amount of Bell peppers.
So, instead, I decided that I was willing to utilize two rows in my seed starting tray. That’s 12 cells.
There are 39 seeds in the packet.
An equal 20%of each variety (orange, white, purple, yellow, and red) included in the packet, according to Burpee.
What are the “odds”, “%chance”, or “probability” (i’ve been thinking about this too long and I’m not even sure which I’m asking for anymore. lol) that I will have planted at least one of each variety?
Please and thank you
If someone made me do math this hard at that age, I would want to piss on my books all the time.
Sorry, but I am so trouble by the way - after so many digressions - you are giving your solving : 4/(2x+1) and 100% to the students providing it.
I am 73, but I clearly remember my math teacher : "you only gave half of the solution! You forgot to provide the restriction : IF X NOT EQUAL TO 1/2”
Dividing numerator and denominator by 2x-1 is only possible with such restriction!
Mohawks were late '70s in the UK what with punk.
Good info for passing academic testing, but of little use in the real world for 86% of today's jobs. Not everyone becomes an engineer, scientist, or math teacher. I achieved a 98 on the NY Regents Algebra test and never used this math in 30 years. I have a calculator.
OMG the South Park Mr. Mackey’s “mmmmkays” - gotta stop with the mmmkays, OK?
I somehow messed up and got +4 as my answer. anyone know what I did wrong?
Of what use is this?
All I can say is thank god for the right-arrow key.
Skip the first ten minutes!
Clear as a Caesar salad. Can't there be an order of operations when doing factoring? Or does it have to be sink-or-swim only? 🤔
I appreciate the video but that still did not make any sense to me at all. I still have no clue what was done.
I remember the 80's! Oh yeah!
skip to 10:08
your welcome
I love the channel 😁
🙂 I'm 64 😊 thank you for reminder ❤
After 37 years I could still use factoring to solve this. However, shouldn't we factor more and the answer would be: 2 / (2X + 1/2)?