Partial fractions on complex function for Laurent series

Question

Whats the proper way to calculate the partial fractions for functions like these

$$ f(z)=\frac{z}{z^2(z+1)} \\ f(z)=\frac{z}{(2-z)^3z} $$

before calculating the Laurent series?

Answer 1

$$\frac z{z^2(z+1)}=\frac1{z(z+1)}=\frac1z-\frac1{z+1}\;--\text{almost no need for calculations: just good "eye"}$$

$$\frac z{(2-z)^3z}=-\frac1{(z-2)^3}\;,\;\text{and this is even more boring than the first one...}$$