I know what the answer is but just can't seem to do the actual decomposition.

Can anyone help?

4x - 4 / (x^{2}-4x+4)

Printable View

- Jul 20th 2012, 06:08 AMtammmylHelp with Partial Fraction Decompostion
I know what the answer is but just can't seem to do the actual decomposition.

Can anyone help?

4x - 4 / (x^{2}-4x+4)

- Jul 20th 2012, 06:26 AMa tutorRe: Help with Partial Fraction Decompostion
Can you factorise the denominator?

- Jul 20th 2012, 06:28 AMskeeterRe: Help with Partial Fraction Decompostion
$\displaystyle \frac{4x-4}{x^2-4x+4} = \frac{4(x-1)}{(x-2)^2} = \frac{A}{x-2} + \frac{B}{(x-2)^2}$

$\displaystyle 4(x-1) = A(x-2) + B$

let $\displaystyle x = 2$ ...

$\displaystyle B = 4$

let $\displaystyle x = 1$

$\displaystyle 0 = -A + 4$

$\displaystyle A = 4$

$\displaystyle \frac{4x-4}{x^2-4x+4} = \frac{4}{x-2} + \frac{4}{(x-2)^2}$ - Jul 20th 2012, 07:13 AMtammmylRe: Help with Partial Fraction Decompostion
Thank you very much!!

You have helped a great deal - now I can finish my assignment.