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Partial Fraction Decomposition

Decompose rational function for distinct linear factors: P(x)/[(x-r1)(x-r2)...]

Input
Result

Enter numerator coeffs and roots.

Technical Description & Theory

What is Partial Fractions Calculator and Why it Matters?

Partial-fraction decomposition reduces rational functions for integration and inverse Laplace transforms.

Mathematical Formula and Theory

P(x)/∏(x−rᵢ) = Σ Aᵢ/(x−rᵢ), with Aᵢ found by the cover-up method.

How to Use This Calculator - Step by Step

  • Enter numerator coefficients and denominator roots.
  • Click Decompose.

Solved Example with Full Calculation

x/[(x−1)(x+1)(x−2)] = −1/(2(x−1)) − 1/(6(x+1)) + 2/(3(x−2)).