Partial Fraction Decomposition

algebra analysis

Definition

Partial Fraction Decomposition

The partial fraction decomposition of a rational fraction is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or serveral fractions with a simpler denominator.

$$\frac{f(x)}{g(x)}=p(x)+\sum _j\frac{f_j(x)}{g_j(x)}$$

where $p(x)$ is a polynomial, and, for each $j$, the denominator $g_j(x)$ is a power of an irreducible polynomial.