Precalculus (6th Edition) Blitzer

For an algebraic expression, a rational expression is an expression which can be expressed in the form $\frac{p}{q}$; here, both $p\ \text{and }q$ are polynomials and the denominator $q\ne 0$.
The quotient of two algebraic polynomials is called a rational expression. For an example, $\frac{x+5}{{{x}^{2}}+x+1}$ Here the numerator is $x+5$ and the denominator is ${{x}^{2}}+x+1$ and ${{x}^{2}}+x+1\ne 0$. Also, take, $\frac{{{x}^{2}}+3x+2}{x+3}$ Here, the numerator is ${{x}^{2}}+3x+2$ and the denominator is $x+3$ and $x+3\ne 0$.