Partial fraction decomposition

Definition

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

5 Must Know Facts For Your Next Test

1. Partial fraction decomposition requires that the degree of the numerator is less than the degree of the denominator.
2. If the denominator has distinct linear factors, each factor gets its own term with an unknown constant in the numerator.
3. For repeated linear factors, terms are included with increasing powers up to the multiplicity of the factor.
4. Quadratic factors in the denominator require terms with linear numerators.
5. Solving for unknown constants involves equating coefficients or substituting suitable values for the variable.

Review Questions

• What is partial fraction decomposition and why is it useful?
• How do you handle repeated linear factors in partial fraction decomposition?
• Describe how to decompose a rational function when the denominator contains irreducible quadratic factors.

Related terms

Rational Function: A function defined by the ratio of two polynomials.

Polynomial Long Division: A method used to divide one polynomial by another, often used before applying partial fraction decomposition.

Integration: \text{The process of finding integrals; partial fractions can simplify integration of complex rational functions.}