Beginning Algebra, 11th Edition

SECTION 7.4 Adding and Subtracting Rational Expressions 445

Subtract numerators.

Distributive property

Combine like terms.

Factor.

= 5 Divide out the common factor.

=

51 x- 52

x- 5

=

5 x- 25

x- 5

=

3 x+ 2 x- 25

x- 5

=

3 x- 1 - 2 x+ 252

x- 5

Subtract the entire

numerator. Use

parentheses to

show this.

Be careful

with signs.

NOW TRY

Subtracting Rational Expressions

Subtract. Write the answer in lowest terms.

Fundamental property

Subtract numerators.

Distributive property

,or

Combine like terms.

Factor the numerator.

12 x+ 1213 x+ 12

1 x- 1221 x+ 12

=

6 x^2 + 5 x+ 1

1 x- 1221 x+ 12

=

6 x^2 + 6 x-x+ 1

1 x- 1221 x+ 12

=

6 x 1 x+ 12 - 11 x- 12

1 x- 1221 x+ 12

=

6 x 1 x+ 12

1 x- 1221 x+ 12

-

11 x- 12

1 x- 121 x- 121 x+ 12

=

6 x

1 x- 122

-

1

1 x- 121 x+ 12

6 x

x^2 - 2 x+ 1

-

1

x^2 - 1

EXAMPLE 9

NOW TRY ANSWERS

8. 3

NOW TRY
EXERCISE 8
Subtract. Write the answer in
lowest terms.

2 m

m- 4

• 
  

m- 12

4 - m

NOW TRY
EXERCISE 9
Subtract. Write the answer in
lowest terms.

5

t^2 - 6 t+ 9

• 
  

2 t

t^2 - 9

9. -^2 t

(^2) + 11 t+ 15
1 t- 3221 t+ 32
Factor the denominators.
or 1 x- 1221 x+ 12
LCD= 1 x- 121 x- 121 x+ 12 ,
NOW TRY
Complete solution available
on the Video Resources on DVD
Concept Check Match each expression in Column I with the correct sum or difference in
Column II.
III

1. 
   
   
   
   2. A. 2 B.
   
   
   
   


2. 
   
   
   
   4. C. D.
   
   
   
   


3. 
   
   
   
   6. E. 1 F. 0
   
   
   
   


4. 
   
   
   
   8. G. H.
   
   
   
   

8 - x

x+ 8

x- 8

8 x

1

8 x

• 
  

1

8 x

1

8

• 
  

1

x

1

x

+

1

8

x

x+ 8

• 
  

8

x+ 8

8 +x

8 x

• 1
  8
  x+ 8


• 
  

  x
  x+ 8

  
  

8

x- 8

• x
  x- 8

x- 8

x+ 8

2 x

x- 8

• 16
  x- 8

x

x+ 8

+

8

x+ 8

7.4 EXERCISES