Key Terms

complex rational expression

A complex rational expression is a rational expression in which the numerator and/or denominator contains a rational expression.

extraneous solution to a rational equation

An extraneous solution to a rational equation is an algebraic solution that would cause any of the expressions in the original equation to be undefined.

proportion

When two rational expressions are equal, the equation relating them is called a proportion.

rational equation

A rational equation is an equation that contains a rational expression.

rational expression

A rational expression is an expression of the form $\frac{p}{q},$ where p and q are polynomials and $q\ne 0.$

rational function

A rational function is a function of the form $R\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$ where $p\left(x\right)$ and $q\left(x\right)$ are polynomial functions and $q\left(x\right)$ is not zero.

rational inequality

A rational inequality is an inequality that contains a rational expression.

similar figures

Two figures are similar if the measures of their corresponding angles are equal and their corresponding sides have the same ratio.

simplified rational expression

A simplified rational expression has no common factors, other than 1, in its numerator and denominator.

zero partition number of a rational inequality

The zero partition number of a rational inequality is a number which makes the rational expression zero or undefined.