Find the Laurent series of $f(z) = \frac{1}{z-2} + \frac{1}{z-3}$ for $2 < |z| < 3$ and for $|z| > 3$ Find the Laurent series of $f(z) = \frac{1}{z-2} + \frac{1}{z-3}$ for $2 < |z| < 3$ and for $|z| > 3$.
Is the first step here to notice that
$$ \frac{1}{z-2} + \frac{1}{z-3} = \frac{2z-5}{(z-2)(z-3)}$$
and compute the Laurent series as a single term rather than in two parts?

Hint: Instead of combining the fractions, think geometric series.
