Rational functions are ratios of two polynomials, for example $(x+5)/(x^2+3)$.
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. 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 $L$.
The set of rational functions over a field $K$ is a field, the field of fractions of the ring of the polynomial functions over $K$.
