Partial Fraction Decomposition Calculator

Decompose rational functions into partial fractions. Enter numerator and denominator polynomials.

Examples: x^2 + 2x + 1, 2x^2 - 3x + 5
Examples: (x+1)(x+2), x^2 + 4x + 4
Partial Fraction Decomposition
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Step-by-Step Solution

Click "Decompose" to see the step-by-step solution.

What is Partial Fraction Decomposition?

Partial fraction decomposition breaks down a rational function into a sum of simpler fractions. It's essential for:

  • 📚 Calculus integration
  • 🧮 Solving differential equations
  • 📈 Laplace transforms
  • 🔧 Engineering mathematics

Common Cases

  • Linear Factors: A/(x-a) + B/(x-b)
  • Repeated Linear: A/(x-a) + B/(x-a)²
  • Quadratic Factors: (Ax+B)/(x²+px+q)
  • Improper Fractions: Polynomial division first

Input Format Guide

  • Use ^ for exponents: x^2 + 2x + 1
  • Use spaces: x^2 + 3x + 2
  • Factor format: (x+1)(x+2)