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.
