Laurent expansions of $1/((z-1)z^2)$

Let \[ f(z)=\frac{1}{(z-1)z^2}, \] which is analytic on \(\mathbb C\setminus\{0,1\}\).

1. Expand \(f\) in a Laurent series valid in a deleted neighborhood of (a) \(z=0\) and (b) \(z=1\).

2. Expand \(f\) in Laurent series centered at \(z=0\) valid in (a) \(0<|z|<1\), (b) \(1<|z|<2\), and (c) \(|z|>2\).