Intermediate Algebra (11th edition)

Adding Rational Expressions

Add.

Factor each denominator.

Add.

Distributive property

=

7 x+ 20

1 x+ 5221 x+ 22

=

5 x+ 10 + 2 x+ 10

1 x+ 5221 x+ 22

=

51 x+ 22 + 21 x+ 52

1 x+ 5221 x+ 22

=

51 x+ 22

1 x+ 5221 x+ 22

+

21 x+ 52

1 x+ 5221 x+ 22

=

5

1 x+ 522

+

2

1 x+ 521 x+ 22

5

x^2 + 10 x+ 25

+

2

x^2 + 7 x+ 10

EXAMPLE 8

SECTION 7.2 Adding and Subtracting Rational Expressions 377

The LCD is

fundamental property

1 x+ 522 1 x+ 22 ;

NOW TRY
EXERCISE 8
Add.
2
m^2 - 6 m+ 9

+

4

m^2 +m- 12

NOW TRY ANSWER

8. 6 m- 4
   1 m- 3221 m+ 42

Combine like terms in

the numerator.

Complete solution available
on the Video Resources on DVD

7.2 EXERCISES

Concept CheckAs review, add or subtract the rational numbers as indicated. Write answers

in lowest terms.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   

4. 5. 6.

Add or subtract as indicated. Write all answers in lowest terms. See Example 1.

7. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20.

21. 22.

Suppose that the expressions given are denominators of fractions. Find the least common

denominator (LCD) for each group. See Example 2.

23. , 24. , 25. , z
    26.k+ 3 , k 27. 2 y+ 8 , y+ 4 28. 3 r- 21 , r- 7

18 x^2 y^324 x^4 y^524 a^3 b^418 a^5 b^2 z- 2

p^3

p^2 - pq+q^2

+

q^3

p^2 - pq+q^2

a^3

a^2 +ab+b^2

-

b^3

a^2 +ab+b^2

5 x+ 6

x^2 +x- 20

+

4 - 3 x

x^2 +x- 20

• 3 p+ 7
  p^2 + 7 p+ 12

+

8 p+ 13

p^2 + 7 p+ 12

y^2

y+ 6

-

36

y+ 6

x^2

x+ 5

-

25

x+ 5

6 y+ 12

4 y+ 3

+

2 y- 6

4 y+ 3

5 x+ 4

6 x+ 5

+

x+ 1

6 x+ 5

6

5 y^4

-

21

5 y^4

9

4 x^3

-

17

4 x^3

7

4 y

-

3

4 y

11

5 x

-

1

5 x

12 t

5

+

s

5

6 x

7

+

y

7

5

r

+

9

r

7

t

+

2

t

3

10

+

7

15

5

18

+

7

12

3

4

-

5

6

5

6

-

8

9

5

16

+

9

16

8

15

+

4

15

NOW TRY