Beginning Algebra, 11th Edition

Step 3 Add the numerators. The LCD is the denominator.

Step 4 Write in lowest terms if necessary.

NOW TRY

Adding Rational Expressions

Add. Write the answer in lowest terms.

Step 1 Since the denominators are different, find the LCD.

The LCD is

is prime.

Step 2 Rewrite each rational expression with the LCD as the denominator.

Multiply the second

fraction by

Distributive property

Step 3

Add numerators.

Keep the same denominator.

Combine like terms.

Step 4

Identity property of

multiplication

Divide out the common

= factors.

1

x- 1

=

11 x+ 12

1 x+ 121 x- 12

=

x+ 1

1 x+ 121 x- 12

=

2 x-x+ 1

1 x+ 121 x- 12

=

2 x

1 x+ 121 x- 12

+

• x+ 1
  1 x+ 121 x- 12

x- 1

x- 1.

=

2 x

1 x+ 121 x- 12

+

• 11 x- 12
  1 x+ 121 x- 12

LCD= 1 x+ 121 x- 12

2 x

x^2 - 1

+

- 1

x+ 1

x+ 1

1 x+ 121 x- 12.

x^2 - 1 = 1 x+ 121 x- 12

2 x

x^2 - 1

+

- 1

x+ 1

EXAMPLE 3

=

11

12 y

=

33

60

, or

11

20

=

8 + 3

12 y

=

5 + 28

60

442 CHAPTER 7 Rational Expressions and Applications

NOW TRY
EXERCISE 3
Add. Write the answer in
lowest terms.

6 t

t^2 - 9

+

• 3
  t+ 3

NOW TRY ANSWERS

2. (a) (b)

3.t-^33

31

35 x

17

30

⎧

⎨

⎩

Remember to

write 1 in the

numerator.

NOW TRY

Adding Rational Expressions

Add. Write the answer in lowest terms.

Factor the

denominators.

The LCD is

= 1 x+ 221 x+ 321 x- 12.

2 x 1 x- 12

1 x+ 221 x+ 321 x- 12

+

1 x+ 121 x+ 22

1 x+ 221 x+ 321 x- 12

=

2 x

1 x+ 221 x+ 32

+

x+ 1

1 x+ 321 x- 12

2 x

x^2 + 5 x+ 6

+

x+ 1

x^2 + 2 x- 3

EXAMPLE 4

NOW TRY
EXERCISE 2
Add. Write each answer in
lowest terms.

(a) (b)

3

5 x

+

2

7 x

5

12

+

3

20

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