Partial fraction

Definition

Partial fractions are a way to decompose a rational function into a sum of simpler fractions. This technique is useful for integrating rational functions or solving certain types of algebraic equations.

5 Must Know Facts For Your Next Test

1. When decomposing into partial fractions, the denominator must be factored completely.
2. The form of the partial fraction decomposition depends on whether the factors in the denominator are linear or quadratic.
3. For repeated linear factors, each factor's power must have its own term in the decomposition.
4. Coefficients in the numerators of partial fractions are determined by equating coefficients after combining the decomposed fractions over a common denominator.
5. Partial fraction decomposition is particularly useful for solving integrals involving rational functions.

Review Questions

Related terms

Rational Function:

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

Integration: The process of finding the integral of a function, often used to find areas under curves.

Linear Factor: A polynomial factor of degree one, such as $(x - a)$.