1. EXAMPLE 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. a. r 2r SOLUTION Divide out common factor. a. r 2r2r = r 2r2r = 1 2 Simplify. ANSWER The excluded value is 0.

2. EXAMPLE 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. b. 5x5x 5(x + 2) SOLUTION b. 5x5x 5(x + 2) = 5x Divide out common factor. Simplify. = x (x + 2) ANSWER The excluded value is – 2.

3. EXAMPLE 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. SOLUTION c. 6m 3 – 12m 3 18m 2 c. 18m 2 6m 3 – 12m 3 = 6m 2 (m – 2) 63m2m2 Factor numerator and denominator. = 6m 2 (m – 2) 6 3 m2m2 Divide out common factor. = m – 2 3 Simplify. ANSWER The excluded value is 0.

4. EXAMPLE 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. SOLUTION d. y 7 – y d. The expression y 7 – y is already in simplest form. ANSWER The excluded value is 7.

5. GUIDED PRACTICE for Example 2 5. 4 a 3 22a 6 SOLUTION 2 2 a 3 2 11 a 3 a 3 = = 2 11 a 3 Divide out common factor. Simplify. ANSWER The excluded value is 0.

6. GUIDED PRACTICE for Example 2 6. 2c2c c + 5 = 2c2c ANSWER The excluded value is – 5.

7. GUIDED PRACTICE for Example 2 7. 2s 2 + 8s 3s +12 2s2s = 3 Factor numerator and denominator. Simplify. ANSWER The excluded value is – 4. = 2s ( s + 4) ( s + 4) 3

8. GUIDED PRACTICE for Example 2 8. 8x8x 8x 3 + 16x 2 8x (x 2 + 2x) 8x8x = 1 x 2 + 2x = ANSWER The excluded value is 0,and – 2.