❖ Partial Fraction Decomposition - Repeated Linear Factor ❖
ฝัง
- เผยแพร่เมื่อ 12 ต.ค. 2024
- Partial Fraction Decomposition - Repeated Linear Factor.
In this video, I do a partial fraction decomposition where the denominator factors are a product of LINEAR and QUADRATIC factors. However, note that the quadratic factor can be factored as a repeated linear factor.
In this case we find the constants A, B, and C that would go with our partial fraction decomposition.
Note that if you are watching this for a Calculus course, I do not perform any actual integration.
![ILLSLICK - WINTER IS COMING [Official Video]](http://i.ytimg.com/vi/dwTMeM1zIhQ/mqdefault.jpg)
Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
Patrick, u definitely did better job than any one of my lecturers. U saved my math subject. Praise for your generosity in teaching.
Almost 10 years old but this is still incredibly helpful, thanks
True
@@adude8883 Is not question of time, remeber you are learnig mathematics from egyptians.
@@hectorgomezyanez6327 bruh what
Now I'm 16 now it's helpful to me
And now it's been 2 years since you posted that comment.
Helped me get through Calc 2 four years ago, and now helped me figure out how to find the derivative of the sigmoid function for a graduate course. I hope future generations find patrickJMT's awesome videos!
Oh we definitely do!
This is when matrices and row reducing saves a lot of time! Excellent video, thank you!
Thank you so much PATRICKJMT !!!! you are like the go to youtuber known in my campus, highly recommended by my peers mathematics&engineering majors. It would SO MUCH FUN, if you include trig partial fraction exercises !!!
I was so confused my teacher was leaving out so many steps. Thank you so much.
They literally skip the entire system of equations part and just write the answer. Here I am thinking this is gonna take 5 minutes to do lol
Thanks for your videos! I use your channel the most when doing calculus homework.
you are welcome and thanks for watching! i appreciate it
Best vid on explaining partial fraction! HIghly Recommended.
Your the best Patrick. Nothing but praise for you.
I finally get it. Thank you, you are a godsend. Hope I can pass the second exam!
patrickJMT is dareal MVP
Thank you so much!, you have no idea how helpful that was; you make it so easy to understand :')
Thank bro I am clearly understand now
I wonder what the guys that don't like this video want. Excellent and free resource . Thank a lot
Why is B's denominator (x+3) and C's denominator (x+3) squared? Shouldn't C's denominator be (x+3) as well?
Thank you very much :3 I always look for your videos when I have an exam and want to understand well
Good work keep going ^^
Damn! Thank you for this. Talking Calc 2 and we are at the point where no one does the steps anymore. We go from problem to answer lol
Well explained sir🙏
2022 first year student has benefited from your video 👏
Thats sarcastic joke at the end tho
Thanks! This video was so helpful I recommend it to all people .Thanks once again .
"The left side is just hangin out." Haha
@crystalakajuicy very happy that i could help : )
12 years, and still helpful
thanks a lot patrick, i feel better with this topic now, now i got new easy way to solve this question thanks again patrick really help me
@TheEazyDuzIt95 I agree. I think that C's denominator has to be (x+3)
Why not just first substitute x=-1 eliminating B and C
Then x==-3 eliminating A and B.
why do we have to use (x+3)^2 for C? why is it to the power of 2 but not 1??
@RUNESCAPEISLIFE S still didn't get it can you clarify please😯😯
Whenever you factor out the denominator as much as possible and you are left with (x+3)^2 , when doing the partial fraction decompision you have to BUILD YOUR WAY UP to the power. So let's assume that you factored out as much as possible and ended up with a denominator of (x+3)^26. You would have to build up to the 26th power by doing a/(x+3)^1 + b/(x+3)^2 ... z/(x+3)^26
Man, you deserve all the best. Damn you did a great job with it. 😍😍👍
Even after 4 years, currently a senior, I come back to this video to review knowledge that I had forgot.
Let’s go pre-calc students!
just want to ask what happened in the denominator of B AND C,why there is still an exponent of 2 in the C where its factor is just (x + 3)(x+3)
It's right but I don't know why
That's what trips me up too
The reason for this is because when you're multiplying out the (x+1)(x+3)^2 to the right side, you need to cancel out (x+3)^2 for the C term, thats why C is only C(x+1) and not C(x+1)(x+3)^-1
Arnel Namoc H
Yah u r write
I'm really thankful for the videos.... They help a lot
If you were to teat the first equation (x+1)+(x+3)+(x+3) as a case 1 (linear) would i get the same answer, or is it totally wrong to do that?
I got A=-3/2, B=-2, and C=1 . I used your guess and check method to make x = -1, and x= -3 in order to cancel out some of the problem and find c and a easily.
Thanks a lot ... you really did cleared my doubt which I had since long and which made me feel partial Fractions are tough due to that doubt...
Thanks again....
Thanks for this .I was confused in taking LCM
Thanks for this video this was very helpful in exams
Thank you soooo much man,this will surely help me with my quiz nextweek
i honestly used the one method he mentioned about subbing values for "x" to cancel certain A,B,C coefficients, it took me 2 min to do the problem
Thanks alot.... May the almighty God bless you 🙏🙏🙏🙏
Thank you very much, I love the way you explain things. So far after khan academy I found you the best, I understand you say:)
Thank you man! You're a great teacher.
U make it look easier using this method
u didnt explain why B only has x+3 as a divider and C has x+2 ^2 divider. this is the most important part of the whole thing!!!
can someone explain me this point please ?
It will be a great help :)
Harsh mk I’m learning too and I have my midterm on Friday. I think you just have to memorize this step. As the exponents build up so (...)^3 would need three fractions?
3 years later and I need to know this answer to this questionnnn. not explained in my textbook or any video I've seen about these problems.
Basically he has taken the LCM of (x+2)^2 which is equal to (x+2)(x+2)^2
And if ur asking why is that only (x+2) is B's divider and (x+2)^2 is C's divider, take it as a common rule to apply here.
Thanks a lot good sir. I mean you said you could also shortcut to solve for A and C, then plug it in the system for B. Would be quicker, thank you for the explanation!
found this 7 days before my final exam,just wanted to say thanks !
Thanks, it's truly helpful!
"What were you doing on Halloween?"
This guy:
Thnx now i can solve partial fraction sums
hi, find your videos really useful, but i just dont seem to be able to grasp how when initially expanding out the brackets into A B and C, the C denominator is (x+3)^2, surely this is could further be factored out into its (X+3)(X+3) components and then we would have too many (X+3)'s i noticed that you mentioned in the previous video (example4) that you said if it was X^20 that there would be A/X^1 + B/X^2 + c/X^3.... all the way upto T/X^20. I simply cannot understand this because if they were all multiplied together they wouldnt equal X^20, they would equal X^20factoral. Thanks for the great videos but im struggling to understand this little part. could you please expand on it a little bit.
Thanks
Yeah I wish someone could explain this. I'm simply doing the steps beause it's what I've been told, with no understanding of why.... :/
welll that escalated quickly.
Thanks alot man as they say old is gold
I have a question...why don't we do long division in this problem? Isn't the numerator supposed to be a degree less than the denominator?
YOU ARE A GENIUS!!!!!! Thank you so much! GOD BLESS YOU!!!!!!
omg thank you so much patrick i owe you my life definitely worth that sub man keep doing what you're doing you helped me sooooooo much
Personally, I noticed that if you foil out the denominator, you get a difference of squares, so I might try factoring out a -10, to reverse the order in the denominator and get rid of the constant, and now I'd have an integral that looks like it'd end up being the inverse tangent hyperbolic function...
Thanks a lot, It's very helpful!!
Superbly explained
thanks ;)
Why do you have to build your way up to the power I can take it as a rule but do you know why that is so?
Awesome vid! Helped me so much with my test :)
tnx tnx a lot you are seen the main point for me 😊
Better understanding. Thanks
After you find A B and C you simply integrate each fraction separately . Normally you get something like A*ln|some function | +/- B*ln|some function| ... etc.
Great video I only had 2 days to learn this in class and we are having a quiz and test in the next 2 days.
thanks, this help me a lot.
thank you very much.
THANKS PATRICK!
Thank u very much
Ur explanation is just woooooo
Excelente explicación , me ayudaste un montón
OH MY GOSH THANK YOU!!! i'm in 9th grade and my parents don't get this, my teacher doesnt explain it well at all, and my classmates are all nerds so they can't explain it well at all haha...
THANK YOU SO MUCH!!! :D
At 7:00 you might have subtracted the 2nd and 3rd equation, and then solve for 1st equation and the result. It would be much simple.
helped me so much ... thank u so much
how would we set up the decomposition if there was only one x^2 variable and nothing else in the numerator?
thanks a lot Patrick you're amazing
How can you remember all this!? By the way, you're the best. Thank you.
so useful bro thankyou
Thanks, didn't learn this
Helped a lot
simple but complete
ALLAH bless u my teacher!
Incredible mann!!!
clear explaination..........thanksssss
There is a easier way to find the constants a, once you get your linear system of equations, simply put into a matrix and put into reduce row echelon form. This will give you your constants quickly
Thanks soo much! I have a question, it might be very silly. How is it that we are allowed to multiply by (-1)? Doesn't this operation mess up the values?
No, it doesn't mess up the values because you're multiplying both sides of the equation by -1. By multiplying both sides, the values remain the same ratio or equivalent as before.
+Inga M
+Michael Tsang I appreciate your answer!
Do we always multiple by (-1) ??
So if I were to solve for A and C before doing the process of equating coefficients and finding their values, could I simply solve for B using any of the two bottom linear equations with plugging in the values of A and B (that were found before equating the coefficients)? It would still give me the correct answer, right?
medo alaa Thanks :)
Thanks sir. So good
Who watching this one 2022 😀
please,upload the derivative method of getting coefficients of PF
to get B,just subtract second & third equation,u get B,substitute in first to get A, and then in C
When you equate the coefficients, can you use a matrix to solve the system patrickjmt?
Sonya Reynolds yes u can. Its much faster. The form is AX=B and u solve by premultiply A^-1 to both sides as (A^-1)A = 1 therefore X=(A^-1)B. This is matrix solution. Easier when you dealing with 4+ variables
Thank you so much ❤
Well explained dude❤️❤️
Awesome.. great explanation...thank you very much
I fucking love you man.. Greetings from Denmark!
why would there be an x+3 and x+3^2 instead of just two x+3
This has yet to be answered
thank you❤️❤️❤️
In example 6 you use Bx + C over the polynomial of degree 2, here (x+3)^2 only gets a C, why is that exactly? Thanks!
Man..u r good @ this..keep it up..
Thank you 🫡🫡
Thanks a lot brother