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  (2)

Cancel threads over sums:

Cancel threads over Boolean combinations of equations and inequalities:

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:

Introduced in 1988
 (1.0)
 |
Updated in 1996
 (3.0)
2007
 (6.0)