Partial Fraction Decomposition Calculator

How the Partial Fraction Decomposition calculator works

Formula. For (mx + n)/((x + a)(x + b)) = A/(x + a) + B/(x + b), matching coefficients gives A + B = m and Ab + Ba = n. Therefore A = (n − ma)/(b − a) and B = m − A.

Example. For 1/((x + 1)(x + 2)), m = 0, n = 1, a = 1, and b = 2. A = (1 − 0)/(2 − 1) = 1 and B = −1, so the result is 1/(x + 1) − 1/(x + 2).

Limitation. This calculator handles only a proper rational expression with two distinct linear factors in the displayed form. It does not handle repeated, irreducible quadratic, or higher-degree factors.