Partial fraction decomposition

Definition

Partial fraction decomposition is a method used to express a rational function as the sum of simpler fractions. This technique is particularly useful for integrating rational functions.

5 Must Know Facts For Your Next Test

1. Partial fraction decomposition applies to proper fractions where the degree of the numerator is less than the degree of the denominator.
2. If the denominator contains distinct linear factors, each factor gets its own term in the decomposition.
3. Repeated linear factors require terms with increasing powers in the denominator (e.g., $\frac{A}{(x-1)} + \frac{B}{(x-1)^2}$).
4. Quadratic and higher-degree irreducible factors require terms with both $Ax+B$ in their numerators.
5. The coefficients for each term in the decomposition are typically found by setting up and solving a system of equations.

Review Questions

• What is partial fraction decomposition used for?
• How do you handle repeated linear factors when performing partial fraction decomposition?
• How can you determine the coefficients in partial fraction decomposition?

Related terms

Rational Function:

A function that can be expressed as the ratio of two polynomials.

System of Equations:

A set of equations with multiple variables which are solved together.

Degree of a Polynomial: The highest power of the variable in a polynomial expression.