The Method of Partial Fractions


Introduction

Early in Algebra you learn how to combine "simple'' fractions into a "more complicated'' one. Here is a typical example:

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The Method of Partial Fractions does the opposite: It dissects a complicated fraction into a sum of simple fractions. While this is a little more complicated than going the other direction, it is also more useful. Major applications of the method of partial fractions include:


How simple can it get?

A simple fraction is a fraction with a simple denominator. The first step consists of detecting the factors (the building blocks) of the given denominator. The Fundamental Theorem of Algebra tells us what is possible: Every polynomial can be factored into linear factors (degree 1 polynomials) and irreducible polynomials of degree 2.

Some Examples.

How can you tell whether a degree 2 polynomial is irreducible (over the field of real numbers), or can be factored further into two linear factors?

There are different methods to decide:


Try it yourself!

Is the polynomial tex2html_wrap_inline477 irreducible or reducible?

Helmut Knaust
Fri Jul 5 13:54:22 MDT 1996

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