I got +1/2 as the numerator of 1/(2-x).
Check this one again.
EDIT: I took the wrong denominator, that is 1/(x-2). Problem resolved later.
I have expressed the expression as partial fractions and I have done binomial expansion up to x cubed. The answer in the book has different coefficients of x squared and x cubed. I have had a good look at it. Can someone check it?