Study Guide and Intervention (continued) - MathnMind

12-2
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention
Rational Expressions
Excluded Values of Rational Expressions
Rational an algebraic fraction whose numerator and
Expression denominator are polynomials
Example:
x 2 1
y 2
Because a rational expression involves division, the denominator cannot equal zero. Any
value of the denominator that results in division by zero is called an excluded value of the
denominator.
State the excluded
State the excluded
4m 8
value of . m 2
values of .
Exclude the values for which m 2 0. Exclude the values for which x
m 2 0 The denominator cannot equal 0.
m 2 2 0 2 Subtract 2 from each side.
m 2 Simplify.
Therefore, m cannot equal 2.
2 9 0.
x2 x
9 0 The denominator cannot equal 0.
(x 3)(x 3) 0 Factor.
x 3 0 or x 3 0 Zero Product Property
3 3
Therefore, x cannot equal 3 or 3.
2 Example 1 Example 2
1
x2 9
Exercises
State the excluded values for each rational expression.
2b
12 a
1. 2.
b 8
32 a
m
3. 4.
2 x 4
2m 8
2 2
x 4
2n 12
2x 18
5.
6.
n2 4
x2 16
x a 1
7. 8.
a2 5a 6
2 4
x2 4x 4
m
9. 10.
2 k 1
2m2 m 1
2 2k 1
k2 4k 3
2x
11. 12.
2 25 n 5x 1
x2 10x 16
2
n2 4n 5
y
13. 14.
2 n y 2
3y2 12
2 2n 3
n2 4n 5
x
15. 16.
2 k 4x 4
4x2 11x 3
2 2k 3
k2 20k 64
© Glencoe/McGraw-Hill 711 Glencoe Algebra 1
Lesson 12-2