Rational Expressions

Introduction and Summary

This chapter deals with rational expressions; that is, with expressions whose numerators and denominators are (or can be written as) polynomials.

The first section explains how to write a rational expression in lowest terms by factoring the numerator and the denominator. We write rational expressions in lowest terms in order to work with them more easily. In addition, writing rational expressions in lowest terms allows us to recognize equivalent expressions.

The second section explains how to add and subtract rational expressions. The process by which we add and subtract rational expressions is similar to the process by which we add and subtract constant fractions.

The next logical step after learning how to add and subtract rational expressions is learning how to multiply and divide rational expressions. This is the focus of section three.

The final section explains how to solve rational equations. A rational equation is formed by setting two rational expressions equal to each other. Solving rational equations is slightly different from solving polynomial equations in that we may come up with solutions which produce zero in a denominator. Since we cannot divide by zero, these solutions must be discarded.

Like polynomials, rational expressions appear frequently in Algebra II and higher mathematics. Thus, we must understand how to perform basic operations with rational expressions and how to solve rational equations.