A rational function is a quotient of two polynomials 
and 
, written
 |
where 
is nonzero. It is sometimes called 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).
