Definition:Rational Function

Definition
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, $S = \R - \left\{{x \in \R: Q \left({x}\right) = 0}\right\}$.

Then the equation $y = \dfrac {P \left({x}\right)} {Q \left({x}\right)}$ defines a function from $S$ to $\R$.

Such a function is called a rational function.