Beginning Algebra, 11th Edition

426 CHAPTER 7 Rational Expressions and Applications

Complete solution available
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Find the numerical value of each rational expression for (a) and (b). See

Example 1.

13.Define rational expressionin your own words, and give an example.

14.Concept Check Fill in each blank with the correct response: The rational expression

is undefined when xis , so. This rational expression is equal to 0

when.

15.Why can’t the denominator of a rational expression equal 0?

16.If 2 is substituted for xin the rational expression , the result is. An often-heard

statement is “Any number divided by itself is 1.” Does this mean that this expression is

equal to 1 for? If not, explain.

Find any values of the variable for which each rational expression is undefined. Write answers

with the symbol. See Example 2.

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20. (a)Identify the two termsin the numerator and the two termsin the denominator of the
    rational expression.
    (b)Describe the steps you would use to write the rational expression in part (a) in lowest
    terms. (Hint:It simplifies to x.)
    30.Concept Check Which one of these rational expressions can be simplified?

A. B. C. D.

Write each rational expression in lowest terms. See Examples 3 and 4.

6 m- 18

7 m- 21

16 x+ 8

14 x+ 7

7 m+ 14

5 m+ 10

1 t+ 521 t- 32

1 t+ 522

1 x+ 121 x- 12

1 x+ 122

151 m- 12

91 m- 12

41 y- 22

101 y- 22

27 p^4

3 p

18 r^3

6 r

x^2 - 5 x

x

x^2 +y^2

y^2

x^2 + 2

2

x^2 + 2

x^2

x^2 + 4 x

x+ 4

4 q+ 2

q^2 + 9

3 x- 1

x^2 + 2

x^2 - 4 x

6

x^2 + 3 x

4

2 r- 5

r^2 - 5 r+ 4

5 m+ 2

m^2 +m- 6

2 x^3

3 x+ 4

4 x^2

3 x+ 5

m- 2

m- 5

x+ 1

x- 6

• 7
  3 z

12

5 y

Z

x= 2

0

0

x- 2

x^2 - 4

x=

xx+- (^53) xZ
x^2 - 9
x^2 - 4
x^2 - 4
x^2 - 9
1 x- 221 x+ 32
1000 x
1 x+ 321 x- 22
500 x
5 x+ 2
4 x^2 - 5 x- 6
7 - 3 x
3 x^2 - 7 x+ 2
1 - 3 x 22
4 x+ 12
1 - 2 x 23
3 x+ 9
2 x^2 - 4 x
3 x- 1
x^2 - 4
2 x+ 1
5 x- 2
4 x
3 x+ 1
5 x
x= 2 x=- 3
7.1 EXERCISES
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