is called a rational function, or sometimes a rational polynomial function. More generally, if
and
are polynomials in multiple variables, their quotient
is called a (multivariate) rational function. The term "rational polynomial"
is sometimes used as a synonym for rational function. However, this usage is strongly
discouraged since by analogy with complex polynomial
and integer polynomial, rational
polynomial should properly refer to a polynomial
with rational coefficients.

A rational function has no singularities other than poles in the extended complex plane. Conversely, if a single-values function has no singularities other
than poles in the extended complex plane,
then it is a rational function (Knopp 1996, p. 137). In addition, a rational
function can be decomposed into partial fractions (Knopp 1996, p. 139).