Beginning Algebra, 11th Edition

Some students prefer Method 1 for problems like Example 2,which is the

quotient of two fractions. They will use Method 2 for problems like Examples 1,

3, 4, and 5,which have sums or differences in the numerators, or denominators,

or both.

Deciding on a Method and Simplifying Complex Fractions

Simplify each complex fraction.

(a)

Distributive property

Fundamental property

Distributive property

= Combine like terms.

3 y+ 2

y+ 8

=

y+ 2 + 2 y

4 y+ 8 - 3 y

=

11 y+ 22 + 2 y

41 y+ 22 - 3 y

a

1

y

b y 1 y+ 22 +a

2

y+ 2

b y 1 y+ 22

a

4

y

b y 1 y+ 22 - a

3

y+ 2

b y 1 y+ 22

=

a

1

y

+

2

y+ 2

b#y 1 y+ 22

a

4

y

• 
  

3

y+ 2

b#y 1 y+ 22

=

1

y

+

2

y+ 2

4

y

• 
  

3

y+ 2

EXAMPLE 6

452 CHAPTER 7 Rational Expressions and Applications

Be careful not to use as the LCD. Because yappears in two denominators, it

must be a factor in the LCD.

y+ 2

There are sums and differences

in the numerator and denominator.

Use Method 2.

Multiply numerator and

denominator by the LCD,

y 1 y+ 22.

(b)

Distributive property

Factor.

= Divide out the common factor.

x+ 1

x- 2

=

1 x- 321 x+ 12

1 x- 321 x- 22

=

x^2 - 2 x- 3

x^2 - 5 x+ 6

a 1 -

2

x

• 3
  x^2

bx^2

a 1 -

5

x

+

6

x^2

bx^2

=

1 -

2

x

• 3
  x^2

1 -

5

x

+

6

x^2

There are sums and differences

in the numerator and denominator.

Use Method 2.

Multiply numerator and

denominator by the LCD, x^2.

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