complex analysis Laurent theorem

Question

I am working on a complex analysis exercice. I need to find the Laurent series centered at z=0 for the function

f(z)=1/(z^2-z)

I cannot see how one can get the result.

Answer 1

We have $f(z)=\frac{1}{z-1}-\frac{1}{z}=\frac{-1}{1-z}-\frac{1}{z}=-\frac{1}{z}+\sum_{n=0}^{\infty}z^n$ for $|z|<1$.