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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
Cite this Page

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[expr,Modulus->p] generates a result modulo p.
  • 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:

Scope  (3)

Cancel threads over sums:

Cancel threads over Boolean combinations of equations and inequalities:

Compute over a finite field:

Options  (3)

Extension  (1)

By default, Cancel treats algebraic numbers as independent variables:

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

Modulus  (1)

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

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

Trig  (1)

By default, Cancel treats trigonometric functions as independent variables:

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

Properties & Relations  (1)

Cancel cancels common factors between numerators and denominators:

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

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_2025_cancel, author="Wolfram Research", title="{Cancel}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/Cancel.html}", note=[Accessed: 16-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_cancel, organization={Wolfram Research}, title={Cancel}, year={2023}, url={https://reference.wolfram.com/language/ref/Cancel.html}, note=[Accessed: 16-August-2025]}