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