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Cancel[expr]

cancels out common factors in the numerator and denominator of expr.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Extension  
Modulus  
Trig  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
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Cancel

Cancel[expr]

cancels out common factors in the numerator and denominator of expr.

Details and Options

  • Cancel cancels out the greatest common divisor of the numerator and denominator.
  • Cancel 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
  • Cancel[expr,Extension->Automatic] allows operations to be performed on algebraic numbers in expr.
  • Cancel[expr,Trig->True] treats trigonometric functions as rational functions of exponentials and manipulates them accordingly.
  • Cancel automatically threads over lists, as well as equations, inequalities and logic functions.

Examples

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Basic Examples  (1)

Cancel common factors:

Wolfram Language code: (x ^ 2 - 1) / (x - 1)
Wolfram Language code: Cancel[%]

Scope  (3)

Cancel threads over sums:

Wolfram Language code: Cancel[(x - y) / (x ^ 2 - y ^ 2) + (x ^ 3 - 27) / (x ^ 2 - 9) + (x ^ 3 + 1) / (x ^ 2 - x + 1)]

Cancel threads over Boolean combinations of equations and inequalities:

Wolfram Language code: Cancel[(x - a) / (x ^ 2 - a ^ 2) == 0 && (x ^ 2 - 2x + 1) / (x - 1) ≥ 0]

Compute over a finite field:

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

Options  (4)

Extension  (2)

By default, Cancel treats algebraic numbers as independent variables:

Wolfram Language code: r = (x ^ 2 - 2) / (Sqrt[2] + x);
Wolfram Language code: Cancel[r]

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

Wolfram Language code: Cancel[r, Extension -> Automatic]

Cancel common factors over a finite field:

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

Modulus  (1)

Over the rational numbers the numerator and the denominator have no common factors:

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

Over the integers modulo 2, the denominator divides the numerator:

Wolfram Language code: Cancel[r, Modulus -> 2]

Trig  (1)

By default, Cancel treats trigonometric functions as independent variables:

Wolfram Language code: Cancel[Sin[2x] / Sin[x]]

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

Wolfram Language code: Cancel[Sin[2x] / Sin[x], Trig -> True]

Properties & Relations  (1)

Cancel cancels common factors between numerators and denominators:

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

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

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_cancel, author="Wolfram Research", title="{Cancel}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/Cancel.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_cancel, organization={Wolfram Research}, title={Cancel}, year={2023}, url={https://reference.wolfram.com/language/ref/Cancel.html}, note=[Accessed: 13-June-2026]}