rational function

Rational function

A rational function $f(x)$ is a function that can be expressed as the ratio of two polynomials:

$$f(x)=\frac{p(x)}{q(x)}=\frac{a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0}{b_m{x}^m+b_{m-1}{x}^{m-1}+\dots +b_{1}x+b_0}$$

where $p(x)$ and $q(x)$ are polynomials with real coefficients, $a_n\ne 0$, $b_m\ne 0$, and $D=\{x\in \mathbb{R}\mid q(x)\ne 0\}$.