College Algebra

study guides for every class

that actually explain what's on your next test

Decomposition

from class:

College Algebra

Definition

Decomposition involves breaking down a complex fraction into simpler partial fractions. This is often used to simplify integration or solve algebraic equations more easily.

congrats on reading the definition of decomposition. now let's actually learn it.

ok, let's learn stuff

5 Must Know Facts For Your Next Test

  1. Partial fraction decomposition is particularly useful for integrating rational functions.
  2. To decompose a fraction, the degree of the numerator must be less than the degree of the denominator.
  3. If the denominator has repeated linear factors, each factor must have a separate term in the decomposition.
  4. For irreducible quadratic factors in the denominator, use terms with linear numerators in the decomposition.
  5. Decomposition requires solving a system of equations to determine the coefficients of the partial fractions.

Review Questions

  • What conditions must be met for a rational function to be decomposed into partial fractions?
  • How do you handle repeated linear factors when performing partial fraction decomposition?
  • Describe how to decompose a rational function with an irreducible quadratic factor in its denominator.

"Decomposition" also found in:

Subjects (68)

© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides