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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 1.4.5, Section 3.3.3.
See also: Together, Cancel, PolynomialQuotient.
Further Examples
Apart splits up expressions into partial fractions.
In[1]:= 
Out[1]= 
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]:= 
Out[4]= 
This uses multiple-angle formulas.
In[5]:= 
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