Intermediate Algebra (11th edition)

Combine like terms in the numerator.

Factor the numerator.

Lowest terms

(b) The LCD is.

Fundamental property

Subtract the numerators.

Distributive property

Combine like terms in the numerator. NOW TRY

=

2

1 q- 121 q+ 12

=

q+ 1 - q+ 1

1 q- 121 q+ 12

=

1 q+ 12 - 1 q- 12

1 q- 121 q+ 12

=

11 q+ 12

1 q- 121 q+ 12

-

11 q- 12

1 q+ 121 q- 12

1 q- 121 q+ 12

1

q- 1

-

1

q+ 1

= 2

=

213 x+ 12

3 x+ 1

=

6 x+ 2

3 x+ 1

SECTION 7.2 Adding and Subtracting Rational Expressions 375

Be careful with signs.

Adding Rational Expressions (Denominators Are Opposites)

Add.

Denominators are opposites.

The LCD is

Add the numerators.

We could use as the common denominator and rewrite the first expression.

The LCD is

NOW TRY

=

- y+ 8

2 - y

, or

8 - y

2 - y

= 2 - y.

- y

2 - y

+

8

2 - y

=

y 1 - 12

1 y- 221 - 12

+

8

2 - y

y

y- 2

+

8

2 - y

=

y- 8

y- 2

= y-2.

y

y- 2

+

- 8

y- 2

=

y

y- 2

+

81 - 12

12 - y 21 - 12

y

y- 2

+

8

2 - y

EXAMPLE 5

Multiply the second expression by .--^11

Multiply the first expression by .--^11

This is an equivalent form of the answer.

NOW TRY
EXERCISE 4
Subtract.

(a)

(b)

5

x- 3

-

5

x+ 3

18 x+ 7 4 x+ 5

-

2 x- 13 4 x+ 5

NOW TRY ANSWERS

(a) 4 (b)

5.tt-- 92 ,or^29 - -tt

30 1 x- 321 x+ 32

NOW TRY
EXERCISE 5
Add.
t
t- 9

+

2

9 - t