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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 1.4.5Section 3.3.3.
  • See also: Together, Cancel, PolynomialQuotient.

    Further Examples

    Apart splits up expressions into partial fractions.

    In[1]:=

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    Here neither x nor y are treated as constants.

    In[2]:=

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    Here y is treated as a constant.

    In[3]:=

    Out[3]=

    Here x is treated as a constant.

    In[4]:=

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    This uses multiple-angle formulas.

    In[5]:=

    Out[5]=