Definition (Rational function)

A rational function $g:\mathbb{R}\to \mathbb{Q}$ is the quotient of two real polynomials $$g(s)=\frac{b_{m}s^{m}+\dots+b_{1}+b_{0}}{s^{n}+a_{n-1}s_{n-1}+\dots+a_{1}s+a_{0}}$$where $a_{k},b_{k}\in\mathbb{R}$, and $m\,\&\,n$ are the degrees of the numerator and denominator polynomials.