split the f(z)=(z^3+1)/(z^2+z) into partial fractions

You can first do a long division to simplify things.

\frac{z^3+1}{z^2 + z} = z-1 + \frac{z+1}{z^2+z}

Then, factorise the denominator;

\frac{z+1}{z(z+1)}

Heh, looks like it's simple than I thought.

Post what you get! :)