Rational Functions

The Wolfram Language can efficiently handle both univariate and multivariate rational functions, with built-in functions immediately implementing standard algebraic transformations.

(RefLink[Apart, paclet:ref/Apart]) — decompose into partial fractions with minimal denominators

(RefLink[Together, paclet:ref/Together]) — put rational functions over a common denominator

(RefLink[Cancel, paclet:ref/Cancel]) — cancel common factors between numerator and denominator

(RefLink[Numerator, paclet:ref/Numerator]), (RefLink[Denominator, paclet:ref/Denominator]) — pick out numerator, denominator

(RefLink[Factor, paclet:ref/Factor]) — factor numerator and denominator, canceling common factors

(RefLink[Expand, paclet:ref/Expand]) — expand everything except denominators

(RefLink[ExpandAll, paclet:ref/ExpandAll]) — expand everything, including denominators

(RefLink[ExpandNumerator, paclet:ref/ExpandNumerator]), (RefLink[ExpandDenominator, paclet:ref/ExpandDenominator]) — expand numerators and denominators only

(RefLink[PadeApproximant, paclet:ref/PadeApproximant]) — find a rational approximation to any function

Operations on Rational Functions