1. The problem statement, all variables and given/known data and the solution (just to check my work) 2. Relevant equations None specifically. There seems to be many ways to solve these problems, but the one used in class seemed to be partial fractions and Taylor series. 3. The attempt at a solution The first step seems to be expanding this using partial fractions, giving me Now, for 0 < |z| < 1, we expand each of the fractions in the parenthesis in powers of z. This is the Laurent series for f (z) which is valid in the region 0 < |z| < 1. I then need to get the other two series, which the next one I should try to get is for the region |z| > 2. To get that, it is suggested that I write the two partial fractions as: However I am not sure what to do with this. I have seen things saying I should expand these two functions, and then add them together, however this does not give me the answer for the region |z| > 2, (in fact, it just gives me the first series, but a degree higher, which makes sense).