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High School
Algebra
Pre-Algebra
Fractions

Brittney Lord

Answered question

2021-10-20

What is the goal of the method of partial fractions?

Answer & Explanation

wheezym

Skilled2021-10-21Added 103 answers

Step 1
The goal of the method of partial fractions is to integrate rational functions (a ratio of polynomials), by expressing it as a sum of simpler fractions, called partial fractions, that we already know how to integrate.
Step 2
For example:

\frac{3 x - 1}{x^{2} - 2 x - 3} = \frac{1}{x + 1} + \frac{2}{x - 3}

\int \frac{3 x - 1}{x^{2} - 2 x - 3} d x = \int \frac{1}{1 + x} + \frac{2}{x - 3} d x

\ln {| x + 1 |} + 2 \ln {| x - 3 |} + C

This example illustrates that if we know how the rational function splits as a sum of simpler functions, we can compute its integral fairly easily.

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