Rational function/Field/Definition

Rational function

Let ${}K$ be a field. For polynomials ${}P,Q\in K[X]$, ${}Q\neq 0$, the function

$D\longrightarrow K,z\longmapsto {\frac {P(z)}{Q(z)}},$

where ${}D$ is the complement of the zeroes of ${}Q$, is called a rational function.