Partial fraction expansion 3 | Partial fraction expansion | Precalculus | Khan Academy

[@tonygorogo478]

I didn't find this video " a bit helpful", I find it "very very very helpful". Thank you.

[@CROFTYNESS]

Thank buddy, these are great refreshers for my exams on Monday and Wednesday! You describe and explain with the upmost excellence, and you’re clean and energetic in your voice. Great aid for thousands of students. Keep it up!

[@93stormer]

I don't know how I got to calculus without knowing how to do partial fractions, but I did. When I was taking integrals, I found that I needed to use this concept, but I didn't know how! Luckily, I had the Khan Academy, which explained partial fractions within a half hour. All I can say is: these videos can help you no matter where you are in your education. Salman Khan, you are the greatest!

[@BadMouton]

I seldom write comments on youtube since its usually pointless, but I sincerely thank god that there are ppl like you in this world, so keep on the good work and rest easy knowing that you're helping a lot of people. Thanks!

[@SN1350]

I wonder if any college professors watch these videos and actually learn a thing or two about teaching, because I have seen some professors that SUCK at teaching. Thanks dude you kick some major ass.

[@aparrotslife]

I cannot thank you enough! You're going to help me get an A in my precalculus class! You're my savior! :)

[@mathematiknet]

The problem in 10:10 is easy to solve. You can figure J, if you put x=a. Then differentiate the equation and put x=a again, to get I,H,G,F,E,D,C,B, A

[@purpletosh]

what a wizard... 'j' IS the tenth letter of the alphabet!

[@francoisbissonnette3482]

BH Smith this guy is a legend

[@abhishekravindra4008]

he idk and gets it spot on J letter 9:57

[@dominator1699]

crazy how a video from 2009 is still better than teachers in 2021

[@johnholme783]

There’s another method of solving partial fractions, it’s called equating the coefficients. I use whatever method is simpler for the particular problem.

[@Tuffadandem]

Sal you are a legend! Thank you so much for these videos.

[@MrShagification]

It's easy if the cubic is something like in the video. But I'm having trouble when the cubic is something like (x+2)^3. I can find C, because A and B both = 0. However, when finding A, the B doesn't = 0 and vice versa.

[@HeeyWhitey]

Sal, you have saved me from certain failure!

[@bebarshosnie8751]

can't get enough of these intuitions 😂

[@imegatrone]

I Really Like The Video From Your Dealing with repeated factors

[@zynthealwavii5084]

This guy is amazing hes funny and helpful,man my grades improved!

[@holyempire08]

this is so helpful. urgh! exams tomorrow.. and I'm glad to say that this has helped me a lot. Keep it up :D

[@vanmanforsman1]

check the first - you use long division, then express it as blah blah + remainder/divisor (the original denominator)

[@Rajivrocks-Ltd.]

First time I heard about this is in Calc 2 for integrating a fraction so now I am finding this vid very very helpful!

[@AnaVazquez428]

Thank you for all of your help Sal. You are doing an amazing gob. I don't know how I would have gotten past Calculus without you.

[@henrydacruz3857]

Thanks....so so so.much. this is why I.love KZbin. When you don't understand it in class, u ll understand at KZbin.... Bless u

[@GangnamStyle60]

My life saver

[@Catbuttttt]

thankkkk you...God bless

[@katherinebcn]

Thank you! You explained it way better than my precalc teacher. Keep it up, finals are coming up soon hahah

[@nicholasm716]

THANK YOU SO MUCH SAL YOU ARE THE BEST PERSON EVER

[@lisagibbon]

as others have said previously and sincerely, thank you!

[@Df994_]

@2i20 This might be a little late but yeah he actually does. It's in partial fraction expansion part 1.

[@owenferrera7295]

great. the lecture provided to us was a bit confusing. this helped a lot

[@aGoooNeR]

I was in class this morning and didn't know what the hell was going on. Now, everything is crystal clear. Thank you very much for these wonderful videos.

[@Mcdonald390]

Actually, this is no special case really as you can actually split the fractions normally as A/(x-1) + B/(x-2) + C/(x-2) and get the same answer. Why? Because all you need to do is add them in order like they appear, as: [A/(x-1) + B/(x-2) ]+ C/ (x-2) I find this method to be straight forward as all you do is carry out you usual cross multiplication. Just keep everything in brackets and choose your values for 'x' in that state as it saves you time rather than expanding the brackets.

[@TheChuggtom88]

thanks so much! i get it now!!!

[@Arham1716]

Please sal Its a humble request to you please make a video on partial fractions with 5 constants .... It would be really useful

[@hjfnation]

that tutorial is quite useful as always

[@doublelunch24]

Thanks, Sal!

[@MrMikees20]

Thks..

[@TheeLavv]

can this guy teach me all of my subjects... forever....

[@RooTHackera]

Thank you so much. I saved me .

[@davidaq6]

indeed the awesome is strong with this one

[@DistortionCG]

I love you

[@td-po5ik]

thanks for this !

[@Daniel-Lin-47]

Thank you

[@lemonsilled7156]

thank you sal

[@mdshakhawathossain2668]

thank you khan

[@kugalojan]

Thank you Khan sir :)

[@caffeineiv4335]

And round 3. 2e^x + 4e^2x + xe^2x minimum passing score, here we come! Thank you

[@PancakeMan123000]

actually I get it now!

[@jjimbodb]

thank you good sir :)

[@Kratos6798]

keeping it stylish

[@SuperMusa1998]

thanks

[@PancakeMan123000]

With the third term of the decomposition: C/(x-2)^2, why is it possible to only use a constant for the numerator? In the previous video he said that the degree of the numerator had to be one less than the denominator, in which case the expression for the numerator would be Cx+D? Could someone explain please?

[@alidostan]

you r just greeeeeeeeeeeeeeat sal :)

[@Carebearbull]

@ledkeb lolol "Hairy", "hit the point home" and there's a third one as well.

[@anonymous-pb2fc]

I will now tell you a magic trick, at around 5:34 or 5:45 when he takes the value of x to be (1)one there instead of 1 take the value to be 2 and instantly all your variables will be canceled out !!!!!

[@niceandwise1474]

+Yusra Sohail i think you can use the constant two at that time and nothing will be changed .

[@2i20]

do u have a video explaining if the numerator's degree was bigger than the denominator's?

[@samibraheem2333]

I'm in LOVE WITH YOU!!!

[@idknuttin]

can we also solve this by doing A/(x-1) + (Bx+C)/(x-2)^2?

[@theajayyy]

A little late, but yes. Expand it and it is the same.

[@kingmurillo]

O.o thanks! :D

[@blumpkin123456789]

hey i have a question how would you find the partial fraction of (2x+9)/(x^2+4x+20). I know theres no factors for the denominator so would u complete the square and get (x+2)^2 + 16?

[@nkolatsis]

You have missed adding number 2 to the series.

[@MellowCruisin]

It didn't look like the numerator was a lower degree than the denomenator in this one? Does it not matter because the denomenator was already factored? I am confused on this

[@khwajaabdurrehman1375]

Isn't the numerator's degree supposed to be less than the denominator's before we can start expanding?

[@Daski69]

the fact that it's C/(x-2)^2 makes perfect sense, but couldn't you also put A/x-1 + Bx+C/(x-2)^2 in that case you'd still have a 1st degree over a 2nd degree, right? thanks!!! ...and all hail the Great Khan

[@mawahebbadawi3819]

for you to put bx+c as your numerator your denominator has to be , 1. not factorise and 2. not factorisable

[@cheechiongfun]

Hey what if you have a denominator value of x^2(x^2+1)?

[@SpenserF]

by the reasoning at 2:34, where B/((x+2)^2) + C/(x+2) = (Bx+C)/((x+2)^2), shouldn't I be able to do A/(x-1) + (Bx+C)/((x+2)^2) and get an equally valid answer? Whenever I try this it doesn't come out

[@marihuano69]

i need your help man, look at this: (2s-1)/s^2(s+1)^3 i know the answer (A=5, B=-1, c=-5, D=-4, E=-3) but im only able to get B and E cos the other letters are multiplied by S^2(s+1)^3 , thx in advance!

[@luisdavid1989]

What if my denominator cannot be factored? Can I still expand the fraction?

[@bwibwi5]

My head. It hurts.

[@knowledgepower7286]

Learn it & you will receive THE POWER

[@jackhughes2345]

You’re clearly stupid then

[@MemeScreen]

Any way you could re-upload it or replace it with the ring in the audio taken out. I was able to do it with one filter in adobe audition. I just think others would appreciate it.

[@minhazmahmud9315]

sir, Why CX + D has not been used in place of C, in the partial fraction C/(x-2)^2 ? here numirator is 2nd degree.....!????

[@martincattell6820]

I know your comment was 8 months ago but still: when the fractions are added together again, B will be multiplied by (x - 2) (to create like terms in its denominator) giving B(x + D) (D = -2) in the numerator anyway. So it is sort of taken care of by having (x - 2)squared under C.

[@climbingcat]

@@martincattell6820 Thanks :) After rewatching the vid, Sal does explain why 1.47 - 2.55

[@TheMikarelax]

does that work with : 1/(x+a)²= 1/ (x+a) + 1/ (x+a)² too ? i mean with + a place of -

[@junkyarddog723]

What!! 2009!!!😲

[@MultiGuitarman21]

how would someone do the partial fraction of this Y(s) = (s+8)/(s+4)^2? I tried this method but i keep getting the wrong numerators. tried several problems actually and seem to only work on some problems. Im clearly doing something wrong. could someone help please thanks

[@mrhappy192]

10th letter is J :D

[@valentinbeleca6096]

this guy...so funny

[@nkhlgeorge]

hey could u pls convert this term into partial fractions for me- 1/[r(r+1)(r+2)(r+3)]

[@anjalbinayak]

How many people are watching it on February 2021?

[@rockandrollkevin]

My intuition is a bit hairy, Sal.

[@neetumishra2632]

what if we had (x-2)^3 in the denominator

[@idknuttin]

watch the end of the video, he explains it

[@paulceltics]

no dislikes :)

[@abeeramir6006]

(x^3+2x+2)÷(x^2+x+1)^2 how to begin that one???

[@magnuschanduru6173]

Use binomial thrm at the bottom and u will get the degree as 4 😝🤭, but still solvable

[@Daski69]

couldn't you write the denominator as (x-1)(x^2-4x+4) and just do (A)/(x-1) + (Bx+C)/(x^2-4x+4) ??? i get why he did it the way he did but I fail to see how the way above is inconsistent... it gives the wrong answer

[@rosep4424]

Why is x set to 0 ?

[@sleepilatanja]

RoseLilly Channel he just thought it was easier to do with zero, you can literally use any number. :)

[@MrTakeUrBitch95]

fucking genius

[@cinquain0]

I don’t know how you turned that ugly equation into something pretty

[@AnaVazquez428]

Oh hush, get your head out of the gutter :)

[@retuzziaro]

Thanks, Sal!

[@keeyishan1995]

Thank you so much!