Beginning Algebra, 11th Edition

SECTION 7.7 Applications of Rational Expressions 467

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x

x- 2

+

3

x+ 2

=

8

x^2 - 4

4 t^2 - t

6 t^2 + 10 t

,

8 t^2 + 2 t- 1

3 t^2 + 11 t+ 10

3

x+ 3

+

4

x+ 6

=

9

x^2 + 9 x+ 18

2

x+ 1

+

5

x- 1

=

10

x^2 - 1

2 k^2 - 3 k

20 k^2 - 5 k

,

2 k^2 - 5 k+ 3

4 k^2 + 11 k- 3

1

m^2 + 5 m+ 6

+

2

m^2 + 4 m+ 3

x+ 2

3

=

2 x- 1

5

5

4 z

• 
  

2

3 z

6

k

• 
  

2

3 k

3

t- 1

+

1

t

=

7

2

OBJECTIVES

Applications of Rational Expressions

7.7

1 Solve problems

about numbers.

2 Solve problems

about distance,

rate, and time.

3 Solve problems

about work.

For applications that lead to rational equations, the six-step problem-solving method

of Section 2.4still applies.

OBJECTIVE 1 Solve problems about numbers.

Solving a Problem about an Unknown Number

If the same number is added to both the numerator and the denominator of the frac-

tion the result is equivalent to Find the number.

Step 1 Readthe problem carefully. We are trying to find a number.

Step 2 Assign a variable.

Let the number added to the numerator and the denominator.

Step 3 Write an equation.The fraction represents the result of adding the

same number to both the numerator and the denominator. Since this result is

equivalent to the equation is written as follows.

Step 4 Solvethis equation.

Multiply by the LCD,

Divide out common factors.

Distributive property

Subtract 2x. Subtract 6.

Step 5 State the answer.The number is 4.

Step 6 Checkthe solution in the words of the original problem. If 4 is added to both

the numerator and the denominator of^25 ,the result is 96 =^23 ,as required.

x= 4

6 + 3 x= 10 + 2 x

312 +x 2 = 215 +x 2

315 +x 2 315 +x 2.

2 +x

5 +x

= 315 +x 2

2

3

2 +x

5 +x

=

2

3

2

3 ,

2 +x

5 +x

x=

2

3.

2

5 ,

EXAMPLE 1

NOW TRY
EXERCISE 1
In a certain fraction, the
numerator is 4 less than the
denominator. If 7 is added to
both the numerator and
denominator, the resulting
fraction is equivalent to
What is the original fraction?

7

8.

NOW TRY ANSWER

1.^2125 NOW TRY