Rational Functions

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

ReferenceReference

Apart decompose into partial fractions with minimal denominators

Together put rational functions over a common denominator

Cancel cancel common factors between numerator and denominator

Numerator, Denominator pick out numerator, denominator

PolynomialRemainder ▪ PolynomialQuotient

Factor factor numerator and denominator, canceling common factors

Expand expand everything except denominators

ExpandAll expand everything, including denominators

ExpandNumerator, ExpandDenominator expand numerators and denominators only

PadeApproximant find a rational approximation to any function

Operations on Rational Functions

Residue ▪ Integrate ▪ Sum

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