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