Intermediate Algebra (11th edition)

(b)

Write with positive exponents.

Use Method 2. Multiply by the LCD,

Use the distributive property in the numerator.

= Lowest terms

1

x^2 y

=

y- 2 x^2

1 y- 2 x^22 x^2 y

x^2 y.

a

1

x^2

-

2

y

b x^2 y

1 y- 2 x^22 x^2 y

=

1

x^2

-

2

y

y- 2 x^2

=

x-^2 - 2 y-^1

y- 2 x^2

384 CHAPTER 7 Rational Expressions and Functions

The 2 does not

go in the

denominator

of this fraction.

Remember to

write 1 in the

numerator.

NOW TRY
EXERCISE 4
Simplify the expression, using
only positive exponents in the
answer.

NOW TRY ANSWER

4. 
   

2 xy- 3 x

x+ 3 y^2

2 y-^1 - 3 y-^2

y-^2 + 3 x-^1

NOW TRY

Complete solution available
on the Video Resources on DVD

7.3 EXERCISES

Concept Check Simplify.

1. 2. 3. 4.

Use either method to simplify each complex fraction. See Examples 1 – 3.

5. 6. 7.

8. 9. 10.

11. 12. 13.

14. 15. 16.

17. 18. 19.

20. 21. 22.

1

x^2

• 1
  y^2
  1
  x

+

1

y

1

b^2

• 1
  a^2
  1
  b


• 
  

  1
  a

  
  

8

t+ 7

24

t^2 - 49

6

y- 4

12

y^2 - 16

4 t^2 - 9 s^2

st

2

s

• 3
  t

x^2 - 16 y^2

xy

1

y

• 4
  x

20 x- 10 y

12 y

2 x-y

6 y^2

8 x- 24 y

10

x- 3 y

5 x

4

t

• 4
  s
  4
  t

• 
  

4

s

3

x

+

3

y

3

x

• 3
  y

4 -

1

p

9 +

5

p

6 +

1

x

7 -

3

x

3 y^2 x^3

8

9 y^3 x^4

16

4 z^2 x^4

9

12 x^2 z^5

15

1 - r

4 r

1 +r

8 r

k+ 1

2 k

3 k- 1

4 k

24

t+ 4

6

t

12

x- 1

6

x

4

3

• 2

1 -

3

8

2 -

1

4

5

4

+ 3

7

8

• 3
  2


• 
  

  1
  4

  
  


• 
  

  3
  8

  
  

5

9

• 1
  3
  2
  3

+

1

6