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EXAMPLE 2

a. ,. 1. 1. 4 r. 4 r. r + 3. r + 3. 4 r = 2 2 r. 10 r 2. 10 r 2. LCM = 2 r 2 5 r = 20 r 2. 10 r 2 = 2 5 r r. ANSWER. The LCD of and is 20 r 2. EXAMPLE 2. Find the LCD of rational expressions. Find the LCD of the rational expressions.

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EXAMPLE 2

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  1. a. , 1 1 4r 4r r + 3 r + 3 4r = 22r 10r2 10r2 LCM = 2 r2 5 r= 20r2 10r2 = 25rr ANSWER The LCD of and is 20r2. EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. SOLUTION a. Find the least common multiple (LCM) of 4rand 10r2. The common factors are circled.

  2. 3x + 4 3x + 4 5 5 b. Find the least common multiple (LCM) of (x – 3)2 b. , x2 – x – 6 x2 – x – 6 (x – 3)2 (x – 3)2 and x2 – x – 6. (x – 3)2 = (x – 3)(x – 3) x2 – 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). EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. SOLUTION

  3. c. Find the least common multiple ofc – 2and2c + 7. c + 8 c + 8 3 3 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). c. , 2c + 7 2c + 7 c – 2 c – 2 ANSWER The LCD of and is (c – 2)(2c + 7). EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. SOLUTION

  4. 1 1 m + 1 m + 1 3. , 4. , 28m 28m 7m3 7m3 2 2 x2 +2 x2 +2 x2 + 4x – 5 x2 + 4x – 5 x2 + 7x + 10 x2 + 7x + 10 ANSWER ANSWER The LCD of and is 28m3. The LCD of and is (x +5)(x – 1)(x + 2). for Example 2 GUIDED PRACTICE Find the LCD of the rational expressions.

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

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