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Partial Fraction Decomposition Calculator

Split a proper rational expression with distinct linear factors into a sum of simple fractions using the cover-up method — with every coefficient and full step-by-step working.

P(x) / [(x − r₁)(x − r₂)…] = A₁/(x − r₁) + A₂/(x − r₂) + …
numerator: x² x constant
over (x −root r₁) (x −root r₂) (x −root r₃)

Enter a proper fraction (numerator degree below the number of factors) over distinct linear factors. Roots must be different.

Results

Partial fraction decomposition
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Step-by-step (cover-up method)