EXAMPLE 1 Find excluded values

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EXAMPLE 1 Find excluded values Find the excluded values, if any, of the expression. b. 2y + 14 5 SOLUTION The expression 5 is undefined when 2y + 14 = 0, or x = – 7. 2y + 14 ANSWER The excluded value is-7.

EXAMPLE 1 Find excluded values Find the excluded values, if any, of the expression. c. v 2 – 9 4v SOLUTION c. The expression 4v is undefined when v2 – 9 = 0, or (v + 3)(v – 3) = 0. The solutions of the equation are – 3 and 3. v2 – 9 The excluded values are – 3 and 3. ANSWER

EXAMPLE 1 Find excluded values Find the excluded values, if any, of the expression. d. 7w + 2 8w 2 + w + 5 SOLUTION d. The expression 7w + 2 8w 2 + w + 5 is undefined when 8w2 + w + 5 = 0 cannot be factored. ANSWER There are no excluded values.

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

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

Simplify expressions by dividing out monomials EXAMPLE 2 Simplify the rational expression, if possible. State the excluded values. c. 6m3 – 12m3 18m2 SOLUTION c. 18m2 6m3 – 12m2 = 6m2 (m – 2) 6 3 m2 Factor numerator and denominator. = 6m2 (m – 2) 6 3 m2 Divide out common factor. = m – 2 3 Simplify. ANSWER The excluded value is 0.

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

GUIDED PRACTICE for Example 2 4 a3 5. 22a6 2 2 a3 SOLUTION = Divide out common factor. = 2 11 a3 Simplify. ANSWER The excluded value is 0.

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

GUIDED PRACTICE for Example 2 2s2 + 8s 7. 3s +12 2s ( s + 4) = 3 Factor numerator and denominator. 2s = 3 Simplify. ANSWER The excluded value is – 4.

GUIDED PRACTICE for Example 2 8x 8x3 + 16x2 8. 8x (x2 + 2x) 8x = 1 x2 + 2x = ANSWER The excluded value is 0,and – 2.