Rational Equations
A rational equation is an equation that contains one or more rational
expressions.
Here are three examples of rational equations.
3
The first step in solving a rational equation is to find the least common
denominator (LCD) of the fractions in the equation.
Procedure
To Find the LCD of the Fractions in an Equation
Step 1 Factor each denominator.
Step 2 List each factor the greatest number of times that it appears
in any one of the denominators.
Step 3 Multiply the factors in the list.
Example 1
Find the LCD of the fractions in this equation:
Solution
Step 1 Factor each denominator.

x^{2}  4
2x
x^{2} + 2x 
= (x + 2)(x  2) = 2 Â· x
= x(x + 2) 
Step 2 List each factor the greatest
number of times that it appears
in any one of the denominators.

x + 2, x  2, 2, x 
Step 3 Multiply the factors in the list. 
2x(x + 2)(x  2) 
So, the LCD is 2x(x + 2)(x  2). 
