Apart

Apart[expr] rewrites a rational expression as a sum of terms with minimal denominators.

Examples

Partial fraction decomposition:

Apart[1/(x^2 - 1)]
(* 1/(2(-1 + x)) - 1/(2(1 + x)) *)

Apart[(x + 1)/(x (x + 2))]
(* 1/(2 x) + 1/(2 (2 + x)) *)

Please visit the official Wolfram Language Reference for more details.