I am to obtain the first 3 terms of the Laurent series about $z = 0$ for:
I know that there is 1 singularity at $z=0$. My denominator is not in a polynomial form so I can convert it into such by taking a Taylor series of the function around z=0 which yields the denominator as:
$$(e^z-1-z) = x^2/2 + x^3/6 + x^4/24 + ...$$
This is the part where I get stuck. I'm supposed to bring that back in and perhaps factor something out of the denominator so the left side is analytic at z=0 and the singularities are shifted to the term on the right side. Any tips on what my next step should be? Many thanks!