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Apart

Apart[expr]
rewrites a rational expression as a sum of terms with minimal denominators.
Apart
treats all variables other than var as constants.
MORE INFORMATION
  • Apart gives the partial fraction decomposition of a rational expression.
  • Apart 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.
EXAMPLESCLOSE ALL
Basic Examples   (1)
Decompose into partial fractions:
Decompose into partial fractions:
In[1]:=
Click for copyable input
Out[1]=
Scope   (3)
Apart can handle symbolic parameters:
Treat as the main variable and as a constant:
Treat as the main variable and as a constant:
Here Apart picks as the main variable and treats as a constant:
Apart threads over equations and inequalities:
Options   (3)
Partial fraction decomposition over the rationals:
Partial fraction decomposition over the integers modulo 2:
Partial fraction decompositions of trigonometric expressions:
Properties & Relations   (1)
Together acts as an inverse of Apart:
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