What is a Rational Expression? Definition and Examples

What is a rational expression? A rational expression is the ratio of a polynomial to another polynomial. 

Therefore, a rational expression can be written in the form  
a polynomial / another polynomial

Here are some good examples of rational expressions

8 / x
x + 3 / x - 5
x + 3 / x2 + 10x + 25

x - 6 / 6 - x
15x2 / 5x + 20
8 - 4x / x2 + 2x - 8

An important thing to remember when dealing with rational expressions is that the value of the expression in the denominator cannot be zero.

Any polynomial / 0
= undefined and undefined means "cannot be found"

A rational expression is in simplest form if the numerator and denominator have no common factors except 1. For example, the following two rational expressions are in simplest form.

x2 + 5 / x + 4
6 / 5x
Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: