Core 4 - Partial fractions question. please help!! :S

Express f(x) = 2 / (2 - 3x + x^2) in partial fractions, ad hence obtain f(x) as a series of ascending powers of x, giving the first four non-zero terms of this expansion. State the set of values of x for which this expansion is valid.

so i have factorised the quadratic and got (2 - x)(1 - x)
but i am a bit confused as to how the partial fraction answer is
(2 / (2 - x)) - (2 / (1 - x))

why is it minus the other fraction? all the other examples in my book are plus. is ita rule when the factorised form has got a number minus x on both of the factor brackets.

and i dont quite understand what to do for the expansion. do i use the binomial expansion method (c4 one) or something else

thanks in advance!!

If you work through the partial fractions, you'll get that the numerator of one is +2, and the other is -2. Putting those values in gives you the result. It's exactly the same as writing:

(2 / (2 - x)) + (-2 / (1 - x))

You're correct in thinking that you just use the binomial expansion for the second part.