Question

partial fraction madness, continuation

Answer 1

method for finding \(b\) in \[\frac{5x^2+20x+6}{x(x+1)^2}=\frac{a}{x}+\frac{b}{x+1}+\frac{c}{(x+1)^2}\]

Answer 2

in terms of a and c and x ?

Answer 3

@mahmit2012 method with derivatives

Answer 4

what's wrong with ordinary method of finding partial differential?

Answer 5

@mahmit2012 had a snap method, but i don't understand it

Answer 6

just a question:

do wolfram has solution?

Answer 7

they have something ugly...

Answer 8

we get \(a=\frac{6}{1}=6\), and \(c=\frac{-9}{-1}=9\) but
\[b=5+0-\frac{6}{(-1)^2}=-1\] step i don't get

Answer 9

http://www.wolframalpha.com/input/?i=integrate+%285x%5E2%2B20x%2B6%29+%2F+%28x%5E3%2B2x%5E2%2Bx%29

Answer 10

oh the original question was an integral, btw.

Answer 11

something to do with a derivative but i don't see it

Answer 12

what's your method for B

Answer 13

is there link to where it was done in snappier way?

Answer 14

looks like the method was, take \[5x^2+20x+6\] divide by \(x\) get
\[5x+20+\frac{x}{6}\] take the derivative get
\[5-\frac{6}{x^2}\] and then evaluate at \(x=-1\)
why this works is going to bug me

Answer 15

but is sure is snapp!

Answer 16

I think we can solve this making three equations....

Answer 17

i meant did you have your own way, satellite?

Answer 18

a slower... sane approach

Answer 19

i plugged in A and C.. expanded it all out... plugged in 1 for x and got B=-3

Answer 20

ooooooooooooooh!!!!
multiply both sides by \((x+1)^2\)!!!!!

Answer 21

but that's not right i guess

Answer 22

wowee zowee

Answer 23

how cool is that? i love it

Answer 24

@alienbrain yes i wrote my method before
solved \(6+B=5\) but it required some visualization