Definition:Rational Function

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

Such a function is called a rational function.