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

2. EXAMPLE 1
Find excluded values
Find the excluded values, if any, of the expression. c.
v 2 – 9 4v
SOLUTION c.
The expression v 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

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

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

10. 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.

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