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Finding the Least Common Denominator of Rational Expressions

To add fractions that have different denominators, we must first write the fractions so that they have the same denominator. We call this denominator the Least Common Denominator or LCD.

Procedure

To Find the Least Common Denominator (LCD) of Rational Expressions

Step 1 Factor each denominator.

Step 2 For each factor, list it the greatest number of times it appears in any factorization.

Step 3 Write the product of the factors in the list.

Example 1

Find the LCD:

Solution

Step 1 Factor each denominator.	x² + x - 6 = (x + 3)(x - 2) x² - x - 2 = (x + 1)(x - 2)
Step 2 For each factor, list it the greatest number of times it appears in any factorization.	x + 3, x - 2, x + 1
Step 3 Write the product of the factors in the list.	(x + 3)(x - 2)(x + 1)
So, the LCD is (x + 3)(x - 2)(x + 1).