Intermediate Algebra (11th edition)

23. 24. 25.

26. 27. 28.

y+ 3

y

• 4
  y- 1
  y
  y- 1

+

1

y

x+ 2

x

+

1

x+ 2

5

x

+

x

x+ 2

p-

p+ 2

4

3

4

• 5
  2 p

y-

y- 3

3

4

9

+

2

3 y

s-r

1

r

1

s

x+y

1

y

+

1

x

SECTION 7.3 Complex Fractions 385

EXERCISES 29 – 34

FOR INDIVIDUAL OR GROUP WORK

Simplifying a complex fraction by Method 1 is a good way to review the methods of

adding, subtracting, multiplying, and dividing rational expressions. Method 2 gives a

good review of the fundamental principle of rational expressions. Refer to the following

complex fraction and work Exercises 29–34 in order.

29.Add the fractions in the numerator.

30.Subtract as indicated in the denominator.

31.Divide your answer from Exercise 29by your answer from Exercise 30.

32.Go back to the original complex fraction and find the LCD of all denominators.

33.Multiply the numerator and denominator of the complex fraction by your answer

from Exercise 32.

34.Your answers for Exercises 31 and 33should be the same. Which method do you

prefer? Explain why.

Simplify each expression, using only positive exponents in your answer. See Example 4.

37. 38.

39. 40.

41. (a)Start with the complex fraction and write it so that there are no nega-

tive exponents in your expression.

(b)Explain why would notbe a correct response in part (a).

(c)Simplify the complex fraction in part (a).

42.Are equivalent? Explain why or why not.

m-^1 +n-^1

m-^2 +n-^2

and

m^2 +n^2

m+n

3

mp-

4

p+

8

m

1

2 m-

1

3 p

3

mp-

4

p+

8

m

2 m-^1 - 3 p-^1

,

a-^2 - 4 b-^2

3 b- 6 a

x-^1 + 2 y-^1

2 y+ 4 x

x-^1 - y-^1

x-^2 - y-^2

x-^2 +y-^2

x-^1 +y-^1

1

p-^2 - q-^2

1

x-^2 +y-^2

4

m

+

m+ 2

m- 1

m+ 2

m

• 2
  m- 1

RELATING CONCEPTS