So in general to find the LCM of expressions in factored form, you may use this formula: (LCM of Expressions) = (Factors with the highest exponent) TIMEs (factors not in common). Okay about your 2nd example and I know that you're not making any reference to the numerator, which is fine, your LCM expression is (x-5)(x-5)(x+4)(x+1) and I agree. But substitute x = 7 (prime number). So if you use this real number, you want to find the LCM OF 16, 22, and 4 (denominators if x = 7) which we know is 176 BUT if we use your predicted (or derived) LCM formula, the LCM comes out to be 352 which is double the real LCM. What gives? Try substituting x = 9 (non-prime) and then try x = 11 (prime), is your expression going to predict the correct LCM value?
When you actually plug in numbers for x, you now have to consider that you may have a gcf between the numerator and denominator that is not 1. For example if you plug in a 7 as you suggested, you get 6/16 which is really 3/8 and 2/4 which is really 1/2. This is what is causing the difference between the two. If you plug in a number where all fractions have a gcf of 1, the formula will predict the LCD correctly, otherwise you have to account for the fact that some of the fractions have a gcf that is not 1. For example if we go to 3/8, 9/22, and 1/2, the LCD is actually 88, not 352 or even 176.
I like the way you factor things. It’s really helpful. Also I felt stupid before watching these two videos. I didn’t understand how to find the LCDs of problems like the ones in this video and I’m a really good Precalculus student. I have an A in there but somehow I didn’t understand something like this. It made me feel so dumb. I get it now though.
You only need the largest number of repeats from any factorization. This occurs when we factor x^2-10x+25. The other two factorizations have only one (x-5).
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So in general to find the LCM of expressions in factored form, you may use this formula: (LCM of Expressions) = (Factors with the highest exponent) TIMEs (factors not in common). Okay about your 2nd example and I know that you're not making any reference to the numerator, which is fine, your LCM expression is (x-5)(x-5)(x+4)(x+1) and I agree. But substitute x = 7 (prime number). So if you use this real number, you want to find the LCM OF 16, 22, and 4 (denominators if x = 7) which we know is 176 BUT if we use your predicted (or derived) LCM formula, the LCM comes out to be 352 which is double the real LCM. What gives? Try substituting x = 9 (non-prime) and then try x = 11 (prime), is your expression going to predict the correct LCM value?
When you actually plug in numbers for x, you now have to consider that you may have a gcf between the numerator and denominator that is not 1. For example if you plug in a 7 as you suggested, you get 6/16 which is really 3/8 and 2/4 which is really 1/2. This is what is causing the difference between the two. If you plug in a number where all fractions have a gcf of 1, the formula will predict the LCD correctly, otherwise you have to account for the fact that some of the fractions have a gcf that is not 1. For example if we go to 3/8, 9/22, and 1/2, the LCD is actually 88, not 352 or even 176.
Thank you so much helps me so much with my online classes and it's amazing that you're still liking comments to this day 8 years lateer
You're so welcome!
I have an exam tommorow, I have been struggling with this kind of LCD since the start, but this helped alot thank you!
Glad it helped! Good luck with your test!
Man I wish I could remember how I did this. It used to be easy.
It comes back quickly.
I like the way you factor things. It’s really helpful. Also I felt stupid before watching these two videos. I didn’t understand how to find the LCDs of problems like the ones in this video and I’m a really good Precalculus student. I have an A in there but somehow I didn’t understand something like this. It made me feel so dumb. I get it now though.
I'm glad it helped, good luck with your studies :)
I struggled learning this in school but you make it so easy and simple keep up the great work!!
I'm really glad it was helpful!
thank you sir for sharing. you're the best so far. i can explain it better now to my students
Yes, you are welcome. Glad it was helpful :)
your videos are super helpful thanks a bunch
You are very welcome! :)
this guy is really amazing. i wish i can meet him in person , thank you so much you made my exams look easier
I'm glad the video was helpful :)
Again, well explained
Glad it was helpful! :)
Can you explain how you got x(x-5)?
We factored x^2-5x, each term has an x that is common: x(x-5)
what if you're supposed to cancel the denominators out by multiplying them to both sides?
Are you trying to solve a Rational Equation? Do you have the example problem you are working on?
Dude I love you, thank you very much for the help
You are very welcome! 😎
better than my teacher!!
Awesome, glad it was helpful!
Thank u so much! This rlly helped!
You are very welcome! Glad it was helpful!
Man,I have online class tomorrow and I can't even understand everything
What problem are you struggling with? I can try to walk you through it.
I get confused because there's 4 (x-5)'s. Can someone clarify for me?
You only need the largest number of repeats from any factorization. This occurs when we factor x^2-10x+25. The other two factorizations have only one (x-5).
thank you it was so helpful
You are very welcome! :)
sir even 1 i dont understan all
What example are you working on? I can try to work through it with you.
Can u answer 2a/ a+2 and 3/a+2
What are you trying to do? The two rational expressions have the same denominator of (a + 2). So that's the LCD.
HOLY FUDGE I LOVE U. THANK U. AHAHSHSHWUWYGSGSGS ITS NOW EASY FOR ME THANK U U MEAN A LOT TO ME OH MY GOD THANK U
You are welcome! 😎
Finally i got ittttt
Awesome, I'm so glad to hear that! :)
nice :)
😎
I have quiz tommorow better pay attention😑😑
Good luck!