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)