§ 6.3

Addition and Subtraction of

Rational Expressions with a

Common Denominator

Angel, Elementary Algebra, 7ed 2

Adding/Subtracting Fractions

0c ,c

ba

c

b

c

a 0c ,

c

ba

c

b

c

a

712

= 512

212

+

Add . 512

212

+

Angel, Elementary Algebra, 7ed 3

Common Denominators

1. Add or subtract the numerators.2. Place the sum or difference of the

numerators found in step 1 over the common denominator.

3. Simplify the fraction if possible.

Subtract .5

6

5

7-2x

5

13-2x

5

6-7-2x

5

6

5

7-2x

Angel, Elementary Algebra, 7ed 4

Common Denominators

a.) Add .12ww

4-2w-

12ww

53w22

Example:

12ww

4-2w-53w

12ww

4-2w-

12ww

53w222

1)(w

1

1)(w

1w2

12ww

4-2w-53w2

Angel, Elementary Algebra, 7ed 5

Common Denominators

b.) Subtract .649x

29x-x

649x

54x2

2

2

2

649x

29)x-(x-54x

649x

29x-x

649x

54x2

22

2

2

2

2

649x

24x3x

649x

29xx-54x2

2

2

22

8)(3x

3)(x

8)8)(3x(3x

8)3)(3x(x

Example:

Angel, Elementary Algebra, 7ed 6

Least Common Denominator

1. Factor each denominator completely. Any factors used more than once should be expressed as powers.

2. List all different factors that appear in any of the denominators. When the same factor appears in more than one denominator, write that factor with the highest power that appears.

3. The least common denominator (LCD) is the product of all the factors listed in step 2.

Angel, Elementary Algebra, 7ed 7

Least Common Denominator

a.)5-x

6

52x

3-x

Find the LCD:

The LCD is (2x + 5)(x – 5).

x

x

xx

2-5x 2

2

b.) The LCD is x(x + 1).x

x

1)x(x

2-5x 2

245 9wz

2

z4w

3c.) The LCD is 36w5z4

.