Intermediate Algebra (11th edition)

79. 80.

Add or subtract as indicated. Write all answers in lowest terms. See Examples 7 and 8.*

8

13 r- 122

+

2

3 r- 1

- 6

3

1 p- 222

-

5

p- 2

+ 4

SECTION 7.2 Adding and Subtracting Rational Expressions 379

*The authors wish to thank Joyce Nemeth of Broward College for her suggestions regarding some of these exercises.

81. 82.

83. 84.

85. 86.

87. 88.

89. 90.

Work each problem.

91.A concours d eleganceis a competition in
which a maximum of 100 points is awarded to a
car on the basis of its general attractiveness. The
function defined by the rational expression

approximates the cost, in thousands of dollars,

of restoring a car so that it will win xpoints.

(a)Simplify the expression for by per-

forming the indicated subtraction.

(b)Use the simplified expression to determine how much it would cost to win 95 points.

92.A cost-benefit modelexpresses the cost of an undertaking in terms of the benefits
received. One cost-benefit model gives the cost in thousands of dollars to remove xper-
cent of a certain pollutant as

.

Another model produces the relationship

.

(a)What is the cost found by averaging the two models? (Hint:The average of two quan-

tities is half their sum.)

(b) Using the two given models and your answer to part (a), find the cost to the nearest

dollar to remove 95% of the pollutant.

(c)Average the two costs in part (b) from the given models. What do you notice about

this result compared with the cost obtained by using the average of the two models?

Simplify. See Section 1.2.

93. 94. 95. 96.

5

6

4

9

3

4

5

12

3

5

6

2

3

4

PREVIEW EXERCISES

1 x= 952

c 1 x 2 =

6.5x

102 - x

c 1 x 2 =

6.7x

100 - x

c 1 x 2

c 1 x 2 =

1010

491101 - x 2

-

10

49

œ

5

x^2 + 6 x+ 9

-

2

x^2 + 4 x+ 3

3

x^2 + 4 x+ 4

+

7

x^2 + 5 x+ 6

3 y

y^2 +yz- 2 z^2

+

4 y- 1

y^2 - z^2

r+s

3 r^2 + 2 rs-s^2

-

s-r

6 r^2 - 5 rs+s^2

6 x+ 5 y

6 x^2 + 5 xy- 4 y^2

-

x+ 2 y

9 x^2 - 16 y^2

5 x-y

x^2 +xy- 2 y^2

-

3 x+ 2 y

x^2 + 5 xy- 6 y^2

6 x

6 x^2 + 5 xy- 4 y^2

-

2 y

9 x^2 - 16 y^2

5 x

x^2 +xy- 2 y^2

-

3 x

x^2 + 5 xy- 6 y^2

2

m^2 - 4 m+ 4

+

3

m^2 +m- 6

3

x^2 - 5 x+ 6

-

2

x^2 - 4 x+ 4