Find a power series around $a=0$ for the function $f:\mathbb{R}\backslash\{2,3\} \to \mathbb{R}$ with $f(x) = \frac{1}{x^2-5x+6}$.
It is
$f(x) = \frac{1}{x^2-5x+6} = \frac{1}{2-x}\frac{1}{3-x} = \frac{1}{1-(x-1)}\frac{1}{1-(x-2)}$
Now I could use the geometric series but I need to take care of the range of $x$ then, right?
$= \sum_{n=0}^{\infty} (x-1)^n \cdot \sum_{n=0}^{\infty} (x-2)^n$
But anyway, I don't know how to proceed from there.. Any hints