Definition:Rational Function/Real

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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.