Cancel[expr] cancels out common factors in the numerator and denominator of expr.
Example: Cancel[(x^2-1)/(x-1)] .
Cancel is Listable.
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.
See The Mathematica Book: Section 1.4.5 and Section 3.3.3.
See also: Apart, GCD.