partial fraction decomposition

Splitting one complicated rational expression back into the simple fractions that were combined to make it.

Partial fraction decomposition reverses the process of combining fractions over a common denominator: given a proper rational expression $\frac{p(x)}{q(x)}$ with $q(x)$ factored, it rewrites the expression as a sum of simpler fractions, one per factor, each with an unknown constant numerator to be solved for by matching coefficients or by the cover-up (Heaviside) method.