Definition:Rational Function

Let $$P: \mathbb{R} \to \mathbb{R}$$ and $$Q: \mathbb{R} \to \mathbb{R}$$ be polynomial functions on the set of real numbers.

Let $$S$$ be the set $$\mathbb{R}$$ from which all the roots of $Q$ have been removed.

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

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

Such an function is called a rational function.