Thread: Power series representation of a function

On ones like this I usually just start with & differentiate and then multiply and divide terms back in to get my final power series, but with the on top, how should I work this? I thought about just factoring out one of the x's on top and setting it outside the series, can I do that?

find your powere series for 1/(x-1)^2 and multiply each term in the result by x^3 so for example a term of the form x^k becomes x^(k+3)