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Together[expr]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Extension  
Modulus  
Trig  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
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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 takes the following options:
  • Extension Nonecoefficient field to be used
    Modulus 0modulus to assume for integers
    Trig Falsewhether to do trigonometric as well as algebraic transformations
  • 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:

Wolfram Language code: Together[a / b + c / d]

Cancel common factors between the numerator and the denominator:

Wolfram Language code: Together[x ^ 2 / (x ^ 2 - 1) + x / (x ^ 2 - 1)]

Scope  (8)

Combine a sum of any number of terms:

Wolfram Language code: Together[(1/x) + (1/x + 1) + (1/x + 2) + (1/x + 3)]

Here all factors of the denominator divide the numerator:

Wolfram Language code: Together[x ^ 2 / (x - y) - x y / (x - y)]

Together threads over lists:

Wolfram Language code: Together[{(1/x) + (1/x + 1), (1/x + 2) + (1/x + 3)}]

Together threads over equations and inequalities:

Wolfram Language code: Together[1 < 1 / x + 1 / (1 + x) < 2]

Compute over the algebraic extension generated by the coefficients:

Wolfram Language code: Together[x ^ 2 / (x - Sqrt[2]) - 2 / (x - Sqrt[2]), Extension -> Automatic]

Compute over the integers modulo :

Wolfram Language code: Together[5x / (3x ^ 2 - y ^ 2) + 3y / (3x ^ 2 - y ^ 2), Modulus -> 3]

Compute over a finite field:

Wolfram Language code: ℱ = FiniteField[17, 3];
Wolfram Language code: Together[x(ℱ[1]x + ℱ[246]) / (ℱ[3]x ^ 2 + ℱ[1771]) + ℱ[4436] / (ℱ[3]x ^ 2 + ℱ[1771])]

Use trigonometric identities:

Wolfram Language code: Together[Sin[x] ^ 2 / Cos[x] + Cos[x], Trig -> True]

Options  (7)

Extension  (3)

By default, Together treats algebraic numbers as independent variables:

Wolfram Language code: Together[(x ^ 2 - 2) / (Sqrt[2] + x)]
Wolfram Language code: Together[1 / (Sqrt[2] + x) + 1 / (x ^ 2 - 2)]

With Extension->Automatic, Together recognizes algebraically dependent coefficients:

Wolfram Language code: Together[(x ^ 2 - 2) / (Sqrt[2] + x), Extension -> Automatic]
Wolfram Language code: Together[1 / (Sqrt[2] + x) + 1 / (x ^ 2 - 2), Extension -> Automatic]

Combine terms and cancel common factors over a finite field:

Wolfram Language code: ℱ = FiniteField[2, 3];
Wolfram Language code: Together[x ^ 4 / (x + 1) + 1 / (x + 1), Extension -> ℱ]

Modulus  (2)

Computations over rational numbers:

Wolfram Language code: Together[1 / x + 1 / (1 + x)]
Wolfram Language code: Together[(x - 1)(x - 2) / ((x - 3)(x - 4)(x - 5))]

The same computations over integers modulo 2:

Wolfram Language code: Together[1 / x + 1 / (1 + x), Modulus -> 2]
Wolfram Language code: Together[(x - 1)(x - 2) / ((x - 3)(x - 4)(x - 5)), Modulus -> 2]

Trig  (2)

By default, Together treats trigonometric functions as independent variables:

Wolfram Language code: Together[1 / Sin[x] + 1 / Cos[x]]

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

Wolfram Language code: Together[1 / Sin[x] + 1 / Cos[x], Trig -> True]

Applications  (1)

Test whether a function is a rational function:

Wolfram Language code: rationalFunctionQ[e_, vars_] := Module[{r = Together[e]}, Apply[And, PolynomialQ[#, vars]& /@ {Denominator[r], Numerator[r]}] ];
Wolfram Language code: rationalFunctionQ[1 / x + y / x, {x, y}]

Properties & Relations  (3)

Apart acts as a partial inverse of Together:

Wolfram Language code: Together[a / b + c / d]
Wolfram Language code: Apart[%]

Together combines terms over a common denominator and cancels common factors:

Wolfram Language code: r = (x - 1) / (x ^ 2 - 1) + (x - 2) / (x ^ 2 - 4);
Wolfram Language code: Together[r]

Cancel only cancels common factors between numerators and denominators:

Wolfram Language code: Cancel[r]

Use Numerator and Denominator to extract numerators and denominators:

Wolfram Language code: expr = Together[1 / x + 1 / y]
Wolfram Language code: Numerator[expr]
Wolfram Language code: Denominator[expr]
Wolfram Research (1988), Together, Wolfram Language function, https://reference.wolfram.com/language/ref/Together.html (updated 2023).

Text

Wolfram Research (1988), Together, Wolfram Language function, https://reference.wolfram.com/language/ref/Together.html (updated 2023).

CMS

Wolfram Language. 1988. "Together." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/Together.html.

APA

Wolfram Language. (1988). Together. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Together.html

BibTeX

@misc{reference.wolfram_2026_together, author="Wolfram Research", title="{Together}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/Together.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_together, organization={Wolfram Research}, title={Together}, year={2023}, url={https://reference.wolfram.com/language/ref/Together.html}, note=[Accessed: 13-June-2026]}