Partial fraction decomposition

Partial fraction decomposition is taking a big algebra fraction and splitting it into a bunch of smaller fractions that are added together. Partial fractions are used to get the antiderivatives of algebra fractions.

In math writing, we're turning this:

${\displaystyle {\frac {f(x)}{g(x)}}}$

Into this:

${\displaystyle {\frac {f_{1}(x)}{g_{1}(x)}}+{\frac {f_{2}(x)}{g_{2}(x)}}+{\frac {f_{3}(x)}{g_{3}(x)}}+\dots +{\frac {f_{i}(x)}{g_{i}(x)}}}$

The denominators of all these fractions are factors of g(x).