Hi. I have to find and classify the isolated singularities for:

$\displaystyle f(z)=\frac{e^z}{1+e^z}$

So, I've found that $\displaystyle e^z=-1\rightarrow{z=i(2k+1)\pi},k\in{Z}$

Now, I think I should make the Laurent series for f(z), but I don't know how to handle this function to get it's Laurent series representation.

I also know, of course, that: $\displaystyle e^z=\sum_0^{\infty}\frac{z^n}{n!}$