Laurent series for $\frac{2}{(z)(z-1)(z-2)}$

Question

! So I think I am getting the hang of Laurent Series, but having a bit of trouble with one of the fractions for part a).

So I split this up in to partial fractions: $\frac{1}{z} - \frac{2}{z-1}+\frac{1}{z-2}$

I am unsure what to do with the last fraction for part a, as if I divided it by 2 I'd have |z/2|<1 or |z| <2 which is obviously not what we want.

Thanks in advance