# Very easy and quick residue calculus question.

## Homework Statement

$$\oint_{\left|z\right|=3/2} \frac{e^{\frac{1}{z-1}}}{z} dz$$

## Homework Equations

Using residue theorem, since there are two singularities withing the domain, evaluate residues at each singularity, and multiply by $$2\pi i$$

## The Attempt at a Solution

Here is the problem. The answer is $$2 \pi i$$ instead of $$2 \pi i + \frac{2\pi i}{e}$$
I don't understand why singularity at zero is ignored.
FYI, if the domain it |z| = 1/2, the answer is 2pi*i/e.