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Section 7.3
Least Common Denominators
Recall how to add or subtract two rational numbers with a common denominator:
Recall how to add or subtract two rational numbers with different denominators:
Before two rational expressions with different denominators can be added or subtracted, both
rational expressions must be expressed in terms of a common denominator. This common
denominator is called the LCD (Least Common Denominator).
How to find the LCD of two (or more) rational expressions:
1) Factor each denominator into prime factors.
2) The LCD is the product of the LCM of the coefficients and each variable factor raised to
the greatest power that occurs in any one factorization.
Example 1
Find the LCD:
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Example 2
Find the LCD:
The next step after finding a common denominator is to rewrite each rational expression with
the new denominator.
Example 3
Rewrite each rational expression with the indicated denominator.
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Example 4
Rewrite each rational expression with the LCD as the denominator.