# Rational expressions

### Definitions

Rational functions are of the form \[ f(x) = \frac{P_{n}(x)}{Q_{m}(x)}\] where \(P_{n} (x)\) and \(Q_{m} (x)\) are polynomial functions of the order \(n\) and \(m\) respectively, and \(Q\) is not the zero function (the function whose output is always zero). For example, simple rational functions are: \[ f(x) = \frac{x+1}{2x^{2}-3x+1}\] or \[ f(x)= \frac{x+1}{x-2}\]