1. 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.

2. 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.

3. 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 – 12m3 =
6m2 (m – 2) 6 3 m2
Factor numerator and denominator. =
6m2 (m – 2) 6 3 m2
Divide out common factors. =
m – 2 3
Simplify.
ANSWER
The excluded value is 0.

4. 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.

5. GUIDED PRACTICE
for Example 2
4 a3
22a6 2
11a3 5.
ANSWER
The excluded value is 0. 6. 2c
c + 5 2c
c + 5
The excluded value is – 5.
ANSWER 2s 3 7.
2s2 + 8s
3s +12
The excluded value is – 4.
ANSWER 8. 8x
8x x2 1
x2 + 2x
The excluded values are
0 and – 2.
ANSWER