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## Homework Statement

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

[/tex]

## Homework Equations

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

## The Attempt at a Solution

Here is the problem. The answer is [tex]2 \pi i[/tex] instead of [tex]2 \pi i + \frac{2\pi i}{e}[/tex]

I don't understand why singularity at zero is ignored.

FYI, if the domain it |z| = 1/2, the answer is 2pi*i/e.