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Together

Together[expr]
puts terms in a sum over a common denominator, and cancels factors in the result.
  • Together makes a sum of terms into a single rational function.
  • The denominator of the result of Together is typically the lowest common multiple of the denominators of each of the terms in the sum.
  • Together avoids expanding out denominators unless it is necessary.
  • Together[expr, Trig->True] treats trigonometric functions as rational functions of exponentials, and manipulates them accordingly.
  • Together automatically threads over lists, as well as equations, inequalities and logic functions.
Combine terms over a common denominator:
Cancel common factors between the numerator and the denominator:
Combine terms over a common denominator:
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Cancel common factors between the numerator and the denominator:
In[1]:=
Click for copyable input
Out[1]=
Combine a sum of any number of terms:
Here all factors of the denominator divide the numerator:
Together threads over equations and inequalities:
By default, Together treats algebraic numbers as independent variables:
With Extension->Automatic, Together recognizes algebraically dependent coefficients:
Computations over rational numbers:
The same computations over integers modulo 2:
By default, Together treats trigonometric functions as independent variables:
With Trig->True, Together recognizes dependencies between trigonometric functions:
Test whether a function is a rational function:
Apart acts as a partial inverse of Together:
Together combines terms over a common denominator and cancels common factors:
Cancel only cancels common factors between numerators and denominators:
Use Numerator and Denominator to extract numerators and denominators:
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