Study Guide and Intervention (continued) - MathnMind

12-2
Simplify Rational Expressions Factoring polynomials is a useful tool for simplifying
rational expressions. To simplify a rational expression, first factor the numerator and
denominator. Then divide each by the greatest common factor.
Example 1
54z 3
24yz
Simplify . 24yz
The GCF of the numerator and the denominator is 6z.
Divide the numerator and denominator by 6z.
9z
Simplify.
2
(6z)(9z
4y
2 (6z)(9z
)
(6z)(4y)
2 )
(6z)(4y)
1
1
Example 2
54z 3
3x 9
Simplify .
State the excluded values of x.
x2 5x 6
3x 9 3(x 3)
Factor.
x2 5x 6 (x 2)(x 3)
3(x 3) 1
Divide by the GCF, x 3.
(x 2)(x 3) 1
3
Simplify.
x 2
Exclude the values for which x 2 5x 6 0.
x 2 5x 6 0
(x 2)(x 3) 0
x 2 or x 3
Therefore, x 2 and x 3.
Exercises
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention (continued)
Rational Expressions
Simplify each expression. State the excluded values of the variables.
7n
1. 2.
3
12ab
a2b2 21n8 m
3. 4.
2 x 2
4
x2 4
m2 6m 8
x
5. 6.
2 2n 8
2x 1
n2 16
x2 1
a
7. 8.
2 x 3a 2
a2 5a 6
2 4
x2 4x 4
m
9. 10.
2 k 2m 1
2m2 m 1
2 1
k2 4k 3
x
11. 12.
2 n x 6
2x2 8
2 25
n2 4n 5
y
13. 14.
2 n y 2
y2 10y 16
2 7n 12
n2 2n 8
© Glencoe/McGraw-Hill 712 Glencoe Algebra 1