EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2 a., 1 4r4r SOLUTION a. Find the least common multiple.

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EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r r 2 a., 1 4r4r SOLUTION a. Find the least common multiple (LCM) of 4r and 10r 2. 4r = 2 2 r The common factors are circled. 10r 2 = 2 5 r r LCM = 2 r 2 5 r = 20r 2 ANSWER The LCD of and is 20r r4r r r 2

EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. 5 (x – 3) 2 b., 3x + 4 x 2 – x – 6 SOLUTION b. Find the least common multiple (LCM) of (x – 3) 2 and x 2 – x – 6. (x – 3) 2 = (x – 3) (x – 3) x 2 – x – 6 = (x – 3) (x + 2) LCM = (x – 3) (x – 3) (x + 2) = (x – 3) 2 (x + 2) ANSWER The LCD of and is (x – 3) 2 (x + 2). 5 (x – 3) 2 3x + 4 x 2 – x – 6

EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. c., 3 c – 2 c + 8 2c + 7 SOLUTION c. Find the least common multiple of c – 2 and 2c + 7. Because c – 2 and 2c + 7 cannot be factored, they don’t have any factors in common. The least common multiple is their product, (c – 2)(2c + 7). ANSWER The LCD of and is (c – 2)(2c + 7). 3 c – 2 c + 8 2c + 7

GUIDED PRACTICE for Example 2 Find the LCD of the rational expressions. m + 1 7m37m3 3., 1 28m ANSWER The LCD of and is 28m m m + 1 7m37m3 4., x x 2 + 7x x 2 + 4x – 5 ANSWER The LCD of and is (x + 5)(x – 1)(x + 2). 2 x 2 + 4x – 5 x x 2 + 7x + 10

GUIDED PRACTICE for Example 2 Find the LCD of the rational expressions. 5., 5a5a a + 3 a + 6 a – 4 ANSWER The LCD of and is (a + 3)(a – 4). 5a5a a + 3 a + 6 a – 4