Partial fraction

Definition

Partial fractions are a way of expressing a rational function as the sum of simpler fractions. This technique is often used to simplify the integration or differentiation of complex expressions.

5 Must Know Facts For Your Next Test

1. Partial fraction decomposition is only applicable to proper rational functions, where the degree of the numerator is less than the degree of the denominator.
2. If the denominator contains irreducible quadratic factors, each quadratic factor will contribute a fraction with a linear numerator in its partial fraction decomposition.
3. Repeated linear factors in the denominator require separate terms for each power up to the highest occurrence in their partial fraction decomposition.
4. Partial fractions can be used to solve systems of equations by breaking down complex rational expressions into simpler components.
5. To find constants in partial fraction decomposition, you can use methods such as equating coefficients or substituting convenient values for variables.

Review Questions

• What is the primary condition for applying partial fraction decomposition to a rational function?
• How do repeated linear factors in the denominator affect partial fraction decomposition?
• What methods can be used to determine constants in partial fraction decomposition?

Related terms

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

Improper Fraction: A rational function where the degree of the numerator is greater than or equal to the degree of the denominator.

Linear Factor: A polynomial factor of degree one.