TITLE: Trouble finding the Laurent Expansion .
QUESTION [1 upvotes]: I'm having trouble progressing through (in my experience) the tedious calculations required to obtain a Laurent Expansion of a complex function.

The problem arises in finding the series within the annulus. Thank you in advanced for your help.

REPLY [2 votes]: Hint for (a): where are the singularities of $f(z)$?
Hint for (b): partial fractions.
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