$Partial Fractions$

Partial Fractions

The decomposition of a rational function into partial fractions with exact coefficients.

f(x) =

A rational function of x: (3x + 5)/(x^2 + 3x + 2), 1/(x (x^2 + 1)).

This calculator decomposes a rational function into partial fractions by the method of unknown coefficients. The coefficients are exact.

Example. (3x + 5) / (x² + 3x + 2) = 2 / (x + 1) + 1 / (x + 2).

The denominator must split into linear factors with rational roots and a power of one quadratic. Otherwise the calculator reports that it gave no exact decomposition.

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