# Together

Together[expr]

puts terms in a sum over a common denominator, and cancels factors in the result.

# Details and Options • 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 is effectively the inverse of Apart.
• Together[expr,Modulus->p] generates a result modulo p.
• Together[expr,Extension->Automatic] allows operations to be performed on algebraic numbers in expr.
• 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.

# Examples

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## Basic Examples(2)

Combine terms over a common denominator:

Cancel common factors between the numerator and the denominator:

## Scope(7)

Combine a sum of any number of terms:

Here all factors of the denominator divide the numerator:

Together threads over lists:

Together threads over equations and inequalities:

Compute over the algebraic extension generated by the coefficients:

Compute over the integers modulo :

Use trigonometric identities:

## Options(6)

### Extension(2)

By default, Together treats algebraic numbers as independent variables:

With , Together recognizes algebraically dependent coefficients:

### Modulus(2)

Computations over rational numbers:

The same computations over integers modulo 2:

### Trig(2)

By default, Together treats trigonometric functions as independent variables:

With Trig->True, Together recognizes dependencies between trigonometric functions:

## Applications(1)

Test whether a function is a rational function:

## Properties & Relations(3)

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: