Key Concepts & Glossary
Key Concepts
- Decompose by writing the partial fractions as . Solve by clearing the fractions, expanding the right side, collecting like terms, and setting corresponding coefficients equal to each other, then setting up and solving a system of equations.
- The decomposition of with repeated linear factors must account for the factors of the denominator in increasing powers.
- The decomposition of with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor, as in .
- In the decomposition of , where has a repeated irreducible quadratic factor, when the irreducible quadratic factors are repeated, powers of the denominator factors must be represented in increasing powers as
.
Glossary
- partial fractions
- the individual fractions that make up the sum or difference of a rational expression before combining them into a simplified rational expression
- partial fraction decomposition
- the process of returning a simplified rational expression to its original form, a sum or difference of simpler rational expressions
Licenses & Attributions
CC licensed content, Specific attribution
- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.