Residue at singularity of this function

Question

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

I am trying to compute the residue of this function at $z = -1$ , I have found it using the residue at infinity theorem , but how do I do it without it ? I mean just by manipulating the numerator so that I can get a Laurent series in powers of $(z+1)$.

Answer 1

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

Can you proceed ?