When finding the Laurent series of $$f(z):=\frac{1}{z(z-1)(z-2)}$$ valid in the region $1<|z-2|<2$ for example do we just use partial fractions to break $f(z)$ up and the just find the Laurent series for each part then add the series' together as per the partial fractions? This seems to make sense to me but I have seen some examples when partial fractions aren't needed so I just wanted to clarify, I guess when partial fractions aren't needed is when the region you want it to be valid on is nice enough; and by that I mean you don't really need to do any manipulations to exploit the geometric series.
Any clarification?