Partial fraction expansion 2 | Partial fraction expansion | Precalculus | Khan Academy

[@tristanc6967]

These popped up in inverse Laplace transforms and I completely forgot how to do them; thanks a bunch!

[@zaidmajeed5292]

there is no need to do long division only a^3-b^3 formula is implemented which is (a^3-b^3)= (a-b)(a^2+ab+b^2)

[@abdurrahman-hi9ex]

Sal doesn't memorize

[@myshitez]

Wow much learning. Many helpful. Very thanks.

[@XavielArt]

Reminds me of Doge meme

[@jirachixu]

CnarFor /r/wooosh

[@BibodhaN]

someone please give this man a nobel prize for his service for humanity!!!! I (and bazzillion other people) would have dropped out of school a long time ago if it wasn't for him.

[@donedeal00051]

Holy smokes, partial fractions just made sense!!!!

[@FalconHaxxors]

I'm actually an engineering student in differential equations doing inverse laplace transformations and I struggled through partial fractions (the supposedly easy part of the problem) until I found your videos. Thanks for the help and keep up the good work!

[@carsenvillegas7259]

SAME

[@trudyandgeorge]

Thank you. This is just so good. I was missing this tool and I need it for integration. Thanks to you I'm up to speed. Thank you thank you thank you thank you.

[@amazingnacho2177]

It’s amazing. It’s either I didn’t pay attention in class in highschool it they didn’t bother going over this. It’s key for integration.

[@DarrenM813]

keep doin what your doin. my lectures notes are useless and i can get literally all the revision from your vids, literally perfect, all questions i had about the subject have been answered. thank you

[@cydonius4010]

I actually said "Sal, how do you know that" at that part

[@mrhitech6742]

Literally the whole reason I came to the video LMAO

[@ПавелГриценко-п6р]

Was this video helpful? Absolutely YES! (my college math teacher sucks)

[@kazihafiz6024]

You could use the cubic function a^3-b^3=(a-b)(a^2+ab+b^2)

[@GenericMedusa99]

4:56 "I've a bad memory" and I am 120 years old

[@ashen_fields]

You are absolutely amazing. This is soo going to help me pass my precalculus final tomorrow.

[@universe378]

Sal, you are providing a great service. The new economy rocks. May riches flow your way.

[@xxchickenboyxx]

Best website in the world. helping alot of people to learn.

[@nicolenicstar]

this helped so much, in nearly cried when i saw the billion and one steps to take in the books, but this really cleared it up. you life saver, you!

[@GlorifiedTruth]

Very well done. And yes, that yellow marker IS vibrant!

[@azznags]

holly crap you make this so much more simpler than the examples in the text book

[@axismage91]

In my understanding,the c's could not be altered to be taken out ( C is not Cx) which would have leave room to solve for B. Instead the B can be taken out when x = 0, BX= B(0)= 0, which would leave the NoT Bx+c(x-2) BUT C(x-2)..(X is now 0)= C(-2) * also dont forgot to factor in the X= o into 10xsquare 2 +12x+20 AND A(x square+2x+4) 20=A(4)+C(-2) And in the lesson we know A=7 20=7(4)+-2c The rest is simple. Plz follow the lesson again to fully understand

[@constancelukwesa5085]

This was too usefull thank you so much 💕💕💕👍👍🙌🙌

[@tonygorogo478]

Thanks a lot. Keep making your videos. They are very helpful.

[@RaniOfCoochNahi]

I feel like a 6-year-old when saying this, BUT...you're my hero and I want to be just like you when I'm older.

[@jgdacashman]

I have never thought about using the method you had just shown to find the expansion of a difference of cubes. Unless I'm dealing with trig functions, I HATE memorizing expansions.. I always get signs mixed up and orders of multiples. So, thank you. :)

[@fr4gr4ncehd32]

Sup Salman! I Luv Ur Vids! it Helps Me Out A Lot! Keep It Going!

[@masouddayaghi5923]

You are wonderful man, if u don't consider it impolite, I like to say that I love you and the way you teach and speak.

[@officialhopsof]

as per usual, this is the best explanation that I have ever seen of this. Thanks.

[@cheechiongfun]

If im not mistaken, the partial fraction has a rule where the the degree of numerator HAS to be lesser than the denominator. This is known as an proper integral.

[@asifsurti9154]

Thank you! It was easy to understand!

[@avehyes7093]

Very helpful and smart work !!

[@MrAssemali]

OMG ~~ tomorrow is my final, and i was so worried about this problem. SAL = you are my hero

[@shailakamat1626]

Thanks I'm a tenth grader who learned calculus thanks to you. I used to get D in math before and now I ace every test

[@pluffy5490]

Thanks sal you saved my life here

[@TheKINGOFCOBRAS]

This is Amazing!!, perfect explanation

[@okabc]

would be awsome if he can win it, but i dont think its for him (not the same category, i think for scientific advances only) but i bet there should be a reward out there for him, so re-shaping the learning system... on second thoughts he could be border line nobel prize

[@aparrotslife]

Thanks a milliion! You make math very easy and fun!

[@thasthakir3125]

a^3+b^3=(a+b)(a^2+ab+b^2)

[@Someguy676]

These videos are great.

[@Suyamu]

great stuff. this will help me with inverse laplace transformations.

[@stareagle36]

If only textbooks could explain this as well as you.

[@caffeineiv4335]

Round 2, many thanks

[@abdi5501boone]

I LOVE YOU! i was reading this damn book for centuries and didn't get this.

[@joshuaex50]

this viedo is very useful! i learn a lot! thank you!!!

[@sumaiyahasannaishavlogging]

I have a question,why improper fractions are to be broken first for finding partial fraction?And when it is directly done like of proper fraction,then why does the result of partial fraction equal to the part of proper fraction and not the improper fraction one?

[@Chris-nq3ri]

Great job explaining this. Thanks.

[@MrMikees20]

Thank you so much.. That was really helpful

[@jubayerhasanmahin9049]

Sal,this was awesome.thanks a lot bro.😊😊

[@SuperLordjulius]

= (x -2)(x ^2+2x+2 ^2)

[@toyboof]

I learned this in 13min while my prof took the entire lecture to explain (but still didn't get it). Thanks

[@DZKun]

Hi What if you have this Question: x-1 / x(x² +2x +5). I tried using the above method but it doesn't work because i can't separate Bx & C. Thanks in advance for any advice

[@alecpapanicolaou9178]

I’m stuck at the same issue

[@alecpapanicolaou9178]

Did you figure it out in the 11 years that have passed? 😂

[@Revanv]

Im your fan! really, thanks!

[@Johanhiggins1]

Give that man a bell's... thanks this really helps!!!

[@random19911004]

x^3-8 is just the difference of two cubes factorisation

[@live688]

awesome, very helpful man

[@ABetterYou1993]

Thank you mr.khanacademy....you the best! Godbless you.=)

[@ktkshahnon6416]

Thank you God.

[@radiosification]

+Ktk Shahnon His name is Sal, not god

[@radiosification]

I get it, but I'm saying don't thank god for Sal's work. He did it himself through his own hard work, without any help from some creator who cannot even be proved to exist.

[@M_Dragon]

you may think he hasn't been proved to exist but that's only because your eyes are blind to all the proof.

[@radiosification]

Daniel Frisch lol

[@carsenvillegas7259]

Thank you

[@jea1080]

if we were left with a remainder would we then split the initial function into two pieces?

[@shootshoot]

my thanks as well sir

[@powninfinity]

Hey sal, If you integrate that ( that = ((7/(x-2))+((3x+4)/(x^2+2x+4))) ) is the best answer/most simplified answer/or even right answer 7ln|x+2|+3xln|x^2+2x+4|+4ln|x^2+2x+4| ?

[@encaluv]

thanks

[@artakisthebest]

Any videos wehre he does integration with partial fractions?

[@david-yt4oo]

6:38 isn't this a perfect square? (i.e. (x+2)^2?). anyways. I've seen a lot of people do the same thing you did, that is, putting that Bx+C term (why?)

[@ryanshimizu9299]

There is no real root to (x^2+2x+4). Doing ((x+2)^2) will factor out to (x^2+4x+4) which isn't the original polynomial. As for the Bx+C...yeah I'm still learning that too lol.

[@samhernandez4513]

I have a bad memory but, let me teach you about partial fractions that i learned in 7th grade lol

[@SigmaBiscuit]

9:42 AWWW YEAH

[@osberttingtiewbing9320]

how can i know that when should i put bx+c or juz constant a,b,c?

[@prakarshsinha1442]

in 5:49 I think it would be easier if we factorize that quad. eq .

[@simonjones7396]

u cant, no real roots

[@kylewagoner]

Difference of cubes!

[@josephmwale3565]

Partial fraction (x^5-3x²+12x-1)/[x³(x²+x+1)(x²+2)³] Help explaining this

[@YoshevElazarMikael]

thanks sir

[@yeti564]

Anyone know why he kept the A and B values when finding C?

[@ashen_fields]

@ShorTyizanAngeL I agree

[@SuperUnicorn12]

hey quick question..anyone can help answer actually....but what do i do when i have a Number with no 'x' with it on the numerator? i.e. 5 / (x - 1) (x + 4)....

[@MossPalone]

Thank you very very very very very very much!!!!!!

[@Itachi21234]

I love you man! (no homo), You rock!

[@Vfdking]

Was there an annotation I missed or has no body noticed that he wrote 12A=84 A=7 Even though it should be A=6 (because 84/12 = 6)

[@スパイシーな男の子]

84/12 = 7. Confirm for yourself with a calculator.

[@Vfdking]

yeah im sorry, and thanks a lot. I feel kinda embarrassed honestly. Not sure what I was thinking when I wrote that.

[@aliazzam626]

Just delete it

[@Soymilllk]

LOL! that was such a long partial fraction!

[@SuperLordjulius]

the way i know is that (x ^3 - 8) = (x ^3-2 ^3)

[@Raiyun166]

Thank you so much for that tip at the beginning for figuring out the factor. I feel so goddamn stupid for never seeing that ~_~ I always just used to try things out.

[@ronald010ify]

@niconikko That's what she said

[@mrmeowmeows7810]

mmmmmmmm very nice

[@burnsyy9119]

4:54... Da fuq? I wish I had what you call a bad memory.

[@Carebearbull]

Thank you, I'm now solving my telescopes. hurray

[@okabc]

0:37-0:40, i am sure no pun intended... who else noticed

[@Afraidofloveandpeace]

Well, I do know Partial Fraction, but I didnt understand it in this vid. Maybe its just me...

[@NinjaNorbe]

You are fcking great man. Better than my old (cool) professor. You really helped me out

[@CharactersInDepth]

a cubed + b cubed has its formula sir. ..

[@Anthony-43]

i now disown my textbook

[@jcf7401]

goated

[@quincy29125]

where did x-2 come from?

[@FLIGHTCOMPANY]

I swear you're a mathamagician.

[@rando1090]

Finals

[@algerianno16]

help me pls, 28200+4y=22x....1 17400+2x=17y....2

[@MrTakeUrBitch95]

hey sal are u khan?

[@niconikko]

Wow, this is a HAIRY problem

[@Blueknightex]

Woah long lol

[@waveboi93]

FUCKING LEGEND

[@samhernandez4513]

nope