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

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