Intermediate Algebra (11th edition)

Solve each equation. See Section 2.1.

43. 
    
    
    
    44. 
        
        
        
        45. 
            
        
        
        
        
    
    
    
    

For each rational function, find all numbers that are not in the domain. Then give the domain,

using set-builder notation. See Section 7.1.

46. 
    
    
    
    47. 48.ƒ 1 x 2 =
    
    
    
    

6

x 2 + 4

ƒ 1 x 2 =

1

x

ƒ 1 x 2 =

1

x^2 - 16

x- 6

5

=

x+ 4

10

x

3

-

x

8

=- 5

1

2

x+

1

4

x=- 9

PREVIEW EXERCISES

386 CHAPTER 7 Rational Expressions and Functions

OBJECTIVES In Section 7.1,we defined the domain of a rational expression as the set of all possi-

ble values of the variable. (We also refer to this as “the domain of the variable.”) Any

value that makes the denominator 0 is excluded.

Equations with Rational Expressions and Graphs

7.4

1 Determine the

domain of the

variable in a

rational equation.

2 Solve rational

equations.

3 Recognize the

graph of a rational

function.

NOW TRY
EXERCISE 1
Find the domain of the
variable in each equation.

(a)

(b)

1

x- 7

+

2

x+ 7

=

14

x^2 - 49

1

3 x

-

3

4 x

=

1

3

OBJECTIVE 1 Determine the domain of the variable in a rational equation.

The domain of the variable in a rational equationis the intersection of the domains

of the rational expressions in the equation.

Determining the Domains of the Variables in Rational

Equations

Find the domain of the variable in each equation.

(a)

The domains of the three rational expressions in the equation are, in order,

and

The intersection of these three domains is all real numbers except 0, written using

set-builder notation as

(b)

The domains of the three expressions are, respectively,

and

The domain of the variable is the intersection of the three domains, all real numbers

except 3 and-3,written 5 x|xZ 36. NOW TRY

5 x|xZ 36 , 5 x|xZ- 36 , 5 x|xZ 36.

2

x- 3

-

3

x+ 3

=

12

x^2 - 9

5 x|xZ 06.

5 x|xZ 06 , 5 x|x is a real number 6 , 5 x|xZ 06.

2

x

-

3

2

=

7

2 x

EXAMPLE 1

is read “positive or

negative,” or “plus or minus.”



OBJECTIVE 2 Solve rational equations.To solve rational equations, we usu-

ally multiply all terms in the equation by the least common denominator to clear the

fractions. We can do this only with equations, not expressions.

NOW TRY ANSWERS

1. (a)
   (b) 5 x|xZ 76

5 x|xZ 06