Rational Expressions
The quotient of two polynomials is called a rational expression. Rational expressions are to polynomials what rational numbers are to integers.
The goal here is to learn to do everything that you do with Rational Numbers with rational expressions. That isn't too difficult as long as you know two things well, rational number arithmetic and polynomial factoring.
Excluded Values
Whenever an expression containing variables is present in the denominator of a fraction, you should be alert to the possibility that certain values of the variables might make the denominator equal to zero, which is forbidden. This means that when we are talking about rational expressions we can no longer say that the variable represents “any real number.”
Simplifying rational expressions
Simplification is also called reducing to lowest terms with number fractions. When you reduce fractions to lowest terms you divide top and bottom by common factors. With algebraic fractions you do the same thing, and you must remember that it is only common factors that you can divide out.
Find out more about rational expressions below.
Practice: Simplify rational expressions in the following exercises.