Question

i need help with partial fractions problem

Answer 1

\[\frac{ 2x }{ (x-1)^3 }\]

Answer 2

@zepdrix @ganeshie8

Answer 3

You have a repeated linear factor in the denominator: \(\large\rm (x-1)\) is linear.
So do you remember how to break that down?

I'll give an example:\[\large\rm \frac{4x+2}{(x+1)^2}=\frac{A}{x+1}+\frac{B}{(x+1)^2}\]And then you would solve for A and B.

Answer 4

\[\large\rm \frac{2x}{(x-1)^3}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C}{(x-1)^3}\]Understand the initial setup? :O

Answer 5

yeah

Answer 6

i used x=1 and got 2 for c is it correct?

Answer 7

mmm yah that sounds right! :)

Answer 8

getting the other 2 looks complicated

Answer 9

Hmm I think I see a neat trick for the other ones :)
Obviously we'd like to avoid expanding everything right?

Answer 10

yeah

Answer 11

okay let me try

Answer 12

Oh I made a boo boo.. my bad :(
\(\large\rm A\ne B\)
I forgot about the C=2 part on the end, woooops.. back up :O

Answer 13

Back to the drawing board >.< woops woops

Answer 14

I still like the idea of plugging in x=0, and x=-1
it will give you a system of 2 equations with A and B.

Answer 15

It's probably about the same amount of work as expanding though

Answer 16

well i have the final answer at the back of the book and its