i am currently ripping my hair out over this, i've checked every corner of the internet and of my book looking for how to do this. i can easily represent functions like 1/(1+x), 5/(1-4x2), 2/(3-x), 4/(2x+3), (x2)/(x4+16), etc, as power series. but i am completely stumped on this...

(x-1)/(x+2)

according to my book the answer is -1/2 sum(n=1 to inf) ((-1n)3xn)/(2n+1) where the interval of convergence "I" = (-2,2)

now ive got the interval by just looking at 1/(x+2) and for 1/(x+2) my equation for a power series representing that is sum(n=0 to inf) (-1)n * (xn) * 1/(2n+1).

any help would be greatly appreciated