rewrites a rational expression as a sum of terms with minimal denominators.


treats all variables other than var as constants.

Details and Options

  • 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[expr,Trig->True] treats trigonometric functions as rational functions of exponentials, and manipulates them accordingly.
  • Apart automatically threads over lists in expr, as well as equations, inequalities, and logic functions.


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Basic Examples  (1)

Decompose into partial fractions:

Click for copyable input

Scope  (3)

Options  (3)

Properties & Relations  (1)

Introduced in 1988
Updated in 2007