\begin{definition}[Definition:Rational Function/Real]
Let $P: \R \to \R$ and $Q: \R \to \R$ be polynomial functions on the set of real numbers.
Let $S$ be the set $\R$ from which all the roots of $Q$ have been removed.
That is:
: $S = \R \setminus \left\{{x \in \R: Q \left({x}\right) = 0}\right\}$.
Then the equation $y = \dfrac {P \left({x}\right)} {Q \left({x}\right)}$ defines a function from $S$ to $\R$.
Such a function is a '''rational function'''.
\end{definition}