\begin{definition}[Definition:Field of Rational Functions]
Let $K$ be a field.
Let $K \sqbrk x$ be the integral domain of polynomial forms on $K$.
Let $\map K x$ be the set of rational functions on $K$:
:$\map K x := \set {\forall f \in K \sqbrk x, g \in K \sqbrk x^*: \dfrac {\map f x} {\map g x} }$
where $K \sqbrk x^* = K \sqbrk x \setminus \set {\text {the null polynomial} }$.
Then $\map K x$ is the '''field of rational functions''' on $K$.
\end{definition}