Rational function/Field/Definition

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

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

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