# Rational function

In mathematics, a **rational function** is any function that can be defined by a **rational fraction**, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field *K*. In this case, one speaks of a rational function and a rational fraction *over K*. The values of the variables may be taken in any field *L* containing *K*. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is *L*.

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The set of rational functions over a field *K* is a field, the field of fractions of the ring of the polynomial functions over *K*.