1.9 Form of partial fractions

Any rational function $f(x)/g(x)$ is equal to:

$\bullet$ a polynomial $p(x)$,

$\bullet$ plus a sum of terms

where $Q(x)$ is an irreducible quadratic such that $Q(x)^{r}$ divides $g(x)$,

$\bullet$ plus a sum of terms of the form

where $b$ is a root of $g(x)$ and $(x-b)^{m}$ divides $g(x)$.