Resolve f(x)= x^2+2x-2/(1-x)(2-x) into a partial fraction.
First divide using long division to get
$\displaystyle 1 + \frac{5x-4}{(1-x)(2-x)}$
Then set up:
$\displaystyle \frac{5x-4}{(1-x)(2-x)} = \frac{A}{1-x} + \frac{B}{2-x}$
according to WolframAlpha the outcome should be:
$\displaystyle \frac{x^2+2x-2}{(1-x)(2-x)} = \frac{6}{(x-2)}+\frac{1}{(1-x)} + 1$