Partial Fraction Decomposition Calculator
Break down rational functions into simpler fractions – ideal for integrals, Laplace transforms, and AP calculus. Get instant decomposition with full steps.
Interactive calculator
Use ^ for powers: 3x^2 - 2x + 1
Use (x-a)^n for repeated roots. Only linear factors supported in this version.
Partial fraction decomposition:
Enter numerator and denominator, then click compute.
Enter numerator and denominator, then click compute.
What is partial fraction decomposition?
Partial fraction decomposition rewrites a rational function as a sum of simpler fractions. Whether you're preparing for AP Calculus BC, solving integrals, or working with inverse Laplace transforms (2026 curriculum), this method is essential. Our partial fraction decomposition calculator with steps handles proper rational expressions with linear denominator factors.
🔢 Why use a decomposition calculator?
- Integration: Break complex integrals into simple logarithmic forms.
- Control theory: Simplify transfer functions.
- AP & College Math: Verify homework step‑by‑step.
- Time‑saving: Avoid tedious algebra for higher-degree polynomials.
📊 Partial fraction cases (2026 reference)
| Denominator factor | Term in decomposition | Example |
|---|---|---|
| Distinct linear (x - a) | A/(x - a) | 3/(x-2) + 5/(x+1) |
| Repeated linear (x - a)ⁿ | A₁/(x-a) + A₂/(x-a)² + ... + Aₙ/(x-a)ⁿ | 2/(x-1) + 3/(x-1)² |
| Irreducible quadratic* | (Ax+B)/(ax²+bx+c) | Coming in 2026 update |
✨ How to use this calculator (exclusive tips)
- Proper fraction required: Degree of numerator must be less than denominator degree. If not, perform polynomial long division first.
- Factor denominator completely into linear factors. Example: (x-2)(x+3)^2
- For repeated roots, the calculator automatically assigns constants A, B, C and solves the linear system.
- Heaviside cover‑up method is used behind the scenes for distinct linear factors.
Pro tip 2026: After decomposition, integrate each term: ∫ A/(x-a) dx = A ln|x-a| + C. Perfect for AP Calculus FRQs.
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Frequently asked questions
What is the best partial fraction decomposition calculator with steps?
Our tool provides full algebraic expansions, coefficient solving, and clear steps — perfect for learning.
Our tool provides full algebraic expansions, coefficient solving, and clear steps — perfect for learning.
Can I use this calculator for integrals?
Yes, the output is ready to integrate term‑by‑term.
Yes, the output is ready to integrate term‑by‑term.
Does it handle repeated linear factors?
Absolutely, e.g., (x-1)²(x+2).
Absolutely, e.g., (x-1)²(x+2).
How to input powers like (x-2)^2?
Use caret: (x-2)^2. The parser understands ^ for exponent.
Use caret: (x-2)^2. The parser understands ^ for exponent.
Is this free and accurate for 2026 exams?
100% free, no registration.
100% free, no registration.