Given $f(z)=\frac{1}{z^2(1-z)}$ I am to find two Laurent series expansions. There are two singularities, $z=0$ and $z=1$. So for the first expansion, I used the region $0<|z|<1$ and I got $\sum_{n=0}^\infty z^n+\frac{1}{z}+\frac{1}{z^2}$. The second expansion is for the region $1<|z|<\infty$. I don't know how to approach this, the explanation in my book is confusing. Any help?
Thanks