Partial Fractions Calculator
Enter a rational expression P(x)/Q(x) where Q is a quadratic. The calculator finds the roots of the denominator and uses them to split the fraction into the sum of two simpler fractions. The discriminant decides whether the result is two real ln-style fractions, a repeated-root fraction, or an already-irreducible quadratic denominator.
Frequently asked questions
What range of denominators is supported?
Degree-2 denominators in this first version. Higher-degree denominators require a polynomial factoring step that we will add in a later release.
What if the numerator has degree ≥ the denominator?
Use the Polynomial Long Division tool first to extract the polynomial quotient, then decompose the remainder over the denominator.
What is the connection to integration?
Partial-fraction decomposition is one of the standard tricks for integrating rational expressions. The Integral Calculator does the decomposition internally when the denominator has degree 2.