I'm learning about series, and there this bit about partial fractions decomposition that I want to ask.
Am I right to assume that, there are multiple way to achieve the form $\frac{A}{1 - \alpha_1x}+\frac{B}{1 - \alpha_2x}$, i.e. there might be several solutions to $(1 - \alpha_1x)(1 - \alpha_2x) = 1 - 3x +x^2$, and hence to $A$ and $B$, but we choose the one most suited to simplify $H(x)$?
If this is true, is there some observation that can make choosing the right set of $\alpha_1,\alpha_2,A,B$ easier?