Partial Fractions Explained

Gihan Marasingha
Mathematical Institute
University of Oxford

Date: 30 December, 2003

Abstract:

I learned about partial fractions in high school and was taught a recipe for expressing a rational function by its partial fraction expansion. I was never taught why the recipe worked, or even given a precise algorithm for carrying out the expansion. In this article, I attempt to fill this gap for inquisitive students.

In what follows, I will be working with polynomials over an arbitrary field $F$. If you don't know what a field is, just think of the reals or the complex numbers. I will denote the degree of a polynomial $f$ by $\partial f$.