A rational function
is a function
that looks like a fraction
and has a variable
in the denominator. The following are examples of rational functions:
Note that a function
is not considered a rational function. Even though it is in the form of a fraction, the denominator does not contain a variable.
Simplifying rational expressions usually involves factoring. Once the expressions have been factored, you can usually divide out common terms and write the expression
in its most simplified form.
All of our examples will have terms that can be divided out. But be careful, this may not always be the case. Some rational expressions will not simplify. Also be aware that sometimes you may need to factor
out a "-1" in some situations that involve terms in the form: (a-b) and (b-a), as in Example #4 below.