Definition:Rational Function

Definition
Let $F$ be a field.

Let $P: F \to F$ and $Q: F \to F$ be polynomial functions on $F$.

Let $S$ be the set $F$ from which all the roots of $Q$ have been removed.

That is:
 * $S = F \setminus \left\{{x \in F: Q \left({x}\right) = 0}\right\}$

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

Such a mapping is called a rational function.

The concept is usually encountered where the polynomial functions $P$ and $Q$ are either real or complex:

Also see

 * Definition:Rational Fraction