Do you mean z^3 +2z^2 - (2z / (z-1) (z-1/2)^2) ? Or z^3 + ((2z^2 -2z) / (z-1) (z-1/2)^2) ? etc.

Please learn some basic latex so that you can better typeset your mathematical expressions:

The code for is [tex]z^3 +2z^2 - \frac{2z}{(z-1) (z-1/2)^2}[/tex].

The code for is [tex]z^3 + \frac{2z^2 -2z}{(z-1) (z-1/2)^2}[/tex].