Help with Partial Fraction Decompostion

**tammmyl** · July 20th 2012, 06:08 AM

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

Can anyone help?

4x - 4 / (x²-4x+4)

**a tutor** · July 20th 2012, 06:26 AM

Can you factorise the denominator?

**skeeter** · July 20th 2012, 06:28 AM

$\frac{4x-4}{x^2-4x+4} = \frac{4(x-1)}{(x-2)^2} = \frac{A}{x-2} + \frac{B}{(x-2)^2}$

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

let $x = 2$ ...

$B = 4$

let $x = 1$

$0 = -A + 4$

$A = 4$

$\frac{4x-4}{x^2-4x+4} = \frac{4}{x-2} + \frac{4}{(x-2)^2}$

**tammmyl** · July 20th 2012, 07:13 AM

Thank you very much!!

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

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