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:<math> f(x) = \frac{P(x)}{Q(x)} </math>
where <math>P</math> and <math>Q</math> are [[polynomial function]]s of <math>x</math> and <math>Q</math> is not the [[zero function]]. The [[___domain of a function|___domain]] of <math>f</math> is the set of all values of <math>x</math> for which the numerator <math>P(x)</math> is defined and the denominator <math>Q(x)</math> is not zero.
However, if <math>\textstyle P</math> and <math>\textstyle Q</math> have a non-constant [[polynomial greatest common divisor]] <math>\textstyle R</math>, then setting <math>\textstyle P=P_1R</math> and <math>\textstyle Q=Q_1R</math> produces a rational function
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