Partial Fraction Decomposition Calculator

This tool splits a proper rational function into partial fractions for three denominator shapes: two different linear factors, three different linear factors, or one repeated linear factor beside a different linear one. You give the numerator coefficients and each factor as its root, so (x - 2) is entered as 2 and (x + 3) as -3, and the answer comes back as the separate terms and as the whole sum. Repeated factors beyond a square, irreducible quadratic factors and improper fractions are outside what it handles, so divide first if the numerator is not lower in degree than the denominator. Coefficients come from the cover-up rule with one derivative for the repeated case, rounded to six decimals.