This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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]:= Out[2]= 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]:= Out[5]=