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12-2 Rational Expressions
(Pages 648–653)
A rational expression is an algebraic fraction whose numerator and
denominator are polynomials. Any values of the variable that result in a
denominator of zero must be excluded from the domain of the variable.
These are called excluded values of the rational expression. To simplify a
rational expression, eliminate (by dividing) any common factors of the
numerator and denominator using the GCF.
Example
b3
Simplify and state the excluded values of b.
2
b 2b 3
b3
b3
b2 2b 3
(b 3)(b 1)
b30
b3
Factor the denominator.
b10
b 1
and
Exclude the values for which b 3 0 and b 1 0.
Therefore, b cannot equal 3 or 1.
1
b3
b3
(b 3)(b 1)
(b 3)(b 1)
Simplify the fraction by dividing by the GCF, b 3.
1
1
b1
, b 1, 3
Try These Together
Simplify and state the excluded values of the variables.
x2 3x 2
2. 2
7a3
1. x 4x 5
14a
HINT: Find the exclude values before you
simplify the expression.
HINT: Factor both the numerator and the
denominator.
Practice
Simplify and state the excluded values of the variables.
6x2y
30x
9x4y2z
x y
5. 2 3
20xyz3
60x yz
10x 5x2
2x
9. 3. 4. 6
12x
7. 8. 2
3x 6
3x 3
x 1
a7
a 9a 14
11. 2
12. 2
8a
a 3a
6. 2
x2 25
x5
10. b2 4
4b 8
x2 6x 8
6x 24
14. 2
y2 7y 6
y 5y 6
13. 2x2 98
15. Standardized Test Practice Simplify the rational expression .
8x 56
x2 49
C B 4(x 7)
x7
D x7
4
6
10 5x
8. , x 0
2x
y1
y1
A 4(x 7)
x2
13. , x 4 14. , y 6, 1 15. D
x2
x
7. 4
, x 2
2
x5
x1
4
a2
b2
3
1
9. x 5, x 5 10. , b 2 11. , x 1, 1 12. , a 7, 2
5
x
3x
a3
2
xy
9yz
x2
1
8
Answers: 1. a, a 0 2. , x 1, 5 3. , x 0 4. 2 x 0, y 0 5. , x 0, y 0, z 0 6. , a 0, 3
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Glencoe/McGraw-Hill
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Glencoe Algebra 1