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.

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.

Examples

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Basic Examples  (1)

Decompose into partial fractions:

Scope  (3)

Apart can handle symbolic parameters:

Treat x as the main variable and y as a constant:

Treat y as the main variable and x as a constant:

Here Apart picks y as the main variable and treats x as a constant:

Apart threads over equations and inequalities:

Options  (3)

Modulus  (2)

Partial fraction decomposition over the rationals:

Partial fraction decomposition over the integers modulo 2:

Trig  (1)

Partial fraction decompositions of trigonometric expressions:

Properties & Relations  (1)

Together acts as an inverse of Apart:

Introduced in 1988
 (1.0)
 |
Updated in 2007
 (6.0)