The problem is to solve fa(x)=(x-1)-2.
The textbook told me to assume an = (c1n+c2)1n.
So from (x-1)-2=c1x/(1-x)-2+c2x/(1-x) (using generating functions for $\displaystyle \sum nx^n$ and $\displaystyle \sum x^n$, I got the equation 1=c1x+c2x(1-x).
But I'm stuck, since the right hand side involves no constant terms.

The textbook says I'm supposed to get n+1.

How can I proceed from the assumption an = (c1n+c2)1n?