Apart

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

Apart[expr, var] treats all variables other than var as constants.

Example: Apart[(x^2+1)/(x-1)] .

Apart gives the partial fraction decomposition of a rational expression.

Apart[expr, var] writes expr as a polynomial in var together with a sum of ratios of polynomials, where the degree in var of each numerator polynomial is less than that of the corresponding denominator polynomial.

Apart[(x + y)/(x - y), x] .

Apart[(x + y)/(x - y), y] .

Apart[expr, Trig -> True] treats trigonometric functions as rational functions of exponentials, and manipulates them accordingly.

See The Mathematica Book: Section 1.4.5 and Section 3.3.3.

See also: Together, Cancel, PolynomialQuotient.

Further Examples