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:

[math]\displaystyle{ \frac{f(x)}{g(x)} }[/math]

Into this:

[math]\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)} }[/math]

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