# Partial Fraction Decomposition Calculator

> Decompose (ax + b) / ((x − r₁)(x − r₂)) into A / (x − r₁) + B / (x − r₂) for distinct linear factors. Returns A, B, and the decomposed form with step notes.

**URL:** https://www.calculatoranswers.com/partial-fraction-decomposition-calculator
**Category:** Education

## Quick Answer

Decompose complex rational expressions into simpler partial fractions. Enter the numerator and denominator polynomials to see the step-by-step algebraic expansion.

## Definition

A partial fraction decomposition calculator is an advanced algebra and calculus utility that breaks down a complex rational function into a sum of simpler rational expressions. The calculator factors the denominator polynomial, determines the appropriate form of the decomposition coefficients based on linear or quadratic factors, and solves the resulting system of linear equations to find the constant numerators. It provides the expanded mathematical steps required to solve for each coefficient. Calculus students use this tool to simplify rational integrands for integration.

## How to Use

1. **Enter the numerator** — Type the polynomial expression representing the numerator of your rational function.
2. **Enter the denominator** — Input the polynomial expression representing the denominator in the second field.
3. **Read the decomposition** — View the final decomposed partial fractions and the step-by-step algebraic expansion.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

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