I need to compute the residue for . I'm going to be using it for Cauchy's residue theorem to evaluate the integral around the circle |z| = 3, so there is obviously a singularity at z=1. I'm confused how to manipulate the fraction and bring in series so that I can see what the coefficient on the term. Thank you.
Hm, yes, thank you for the hint. However, the formula using the poles is three chapters after the section we are currently working on. This definitely makes the most sense to use though, so hopefully, I won't be penalized for using a different method. Thank you again