Beginning Algebra, 11th Edition

Step 1 Find the LCD for all denominators in the complex fraction.

The LCD for 3, 9, 4, and 12 is 36. The LCD for x, 4, and 8 is 8x.

Step 2

Multiply.

or or

24

x

=

2412 x+ 12

x 12 x+ 12

,

11

3

=

44

12

=

4 # 11

4 # 3

,

=

48 x+ 24

2 x^2 +x

=

24 + 20

9 + 3

8 x 162 + 8 xa

3

x

b

8 xa

x

4

b+ 8 xa

1

8

b

=

36 a

2

3

b+ 36 a

5

9

b

36 a

1

4

b+ 36 a

1

12

b

=

8 xa 6 +

3

x

b

8 xa

x

4

+

1

8

b

=

36 a

2

3

+

5

9

b

36 a

1

4

+

1

12

b

=

6 +

3

x

x

4

+

1

8

2

3

+

5

9

1

4

+

1

12

SECTION 7.5 Complex Fractions 451

Multiply numerator and

denominator of the complex

fraction by the LCD.

Simplifying Complex Fractions (Method 2)

Simplify each complex fraction.

(a) (b)

6 +

3

x

x

4

+

1

8

2

3

+

5

9

1

4

+

1

12

EXAMPLE 4

(In Example 1,we simplified

these same fractions using

Method 1.)

Distributive

property

Multiply

each

term

by 36.

Multiply

each

term

by 8x.

NOW TRY

NOW TRY
EXERCISE 4
Simplify each complex
fraction.

(a) (b)

2

x

• 3

7 +

x

5

3

5

• 1
  4
  1
  8

• 3
  20

NOW TRY ANSWERS

4. (a) (b)^10 -^15 x
   x^2 + 35 x

14

11

Simplifying a Complex Fraction (Method 2)

Simplify the complex fraction.

Distributive property.

= Multiply and simplify.

12 m - 40

90 m + 15

20 m^2 a

3

5 m

b- 20 m^2 a

2

m^2

b

20 m^2 a

9

2 m

b+ 20 m^2 a

3

4 m^2

b

=

20 m^2 a

3

5 m

• 2
  m^2

b

20 m^2 a

9

2 m

+

3

4 m^2

b

=

3

5 m

• 2
  m^2
  9
  2 m

• 
  

3

4 m^2

EXAMPLE 5

The LCD for 5m,

2 m, and 4 m^2 is 20m^2.

m^2 ,

Multiply numerator and

denominator by 20m^2.

NOW TRY
EXERCISE 5
Simplify the complex
fraction.
1
y

• 2
  3 y^2
  5
  4 y^2

• 3
  2 y^3

5. 
   

12 y^2 + 8 y

15 y- 18

NOW TRY