Beginning Algebra, 11th Edition

(Marvins-Underground-K-12) #1
Adding Rational Expressions (Same Denominator)
Add. Write each answer in lowest terms.

(a) (b)

The denominators are the same, so the sum is found by adding the two numera-
tors and keeping the same (common) denominator.

Add. Add.

Factor.

Factor.

Lowest terms

Lowest terms
NOW TRY

=

2

3

= 3

=

2 # 3
3 # 3

=

31 x+ 12
x+ 1

=

6

9

=

3 x+ 3
x+ 1

=

4 + 2

9

3 x
x+ 1

+

3

x+ 1

4

9

+

2

9

EXAMPLE 1

SECTION 7.4 Adding and Subtracting Rational Expressions 441

NOW TRY
EXERCISE 1
Add. Write each answer in
lowest terms.


(a)


(b)


4 y
y+ 3

+

12
y+ 3

2
7 k
+

4
7 k

NOW TRY ANSWERS



  1. (a) 76 k (b) 4


OBJECTIVE 2 Add rational expressions having different denominators.
As in Section 1.1,we use the following steps to add fractions having different
denominators.

Adding Rational Expressions (Different Denominators)

Step 1 Find the least common denominator (LCD).


Step 2 Rewrite each rational expressionas an equivalent rational expres-


sion with the LCD as the denominator.


Step 3 Addthe numerators to get the numerator of the sum. The LCD is


8.4 Rationalizing the Denominator


Step 4 Write in lowest termsusing the fundamental property.


Adding Rational Expressions (Different Denominators)
Add. Write each answer in lowest terms.

(a) (b)

Step 1 First find the LCD, using the methods of the previous section.

Step 2 Now rewrite each rational expression as a fraction with the LCD (60 and
12 y, respectively) as the denominator.

=

8

12 y

+

3

12 y

=

5

60

+

28

60

2

3 y

+

1

4 y

=

2142

3 y 142

+

1132

4 y 132

1

12

+

7

15

=

1152

12152

+

7142

15142

LCD= 22 # 3 # 5 = 60 LCD= 22 # 3 #y= 12 y


15 = 3 # 5 4 y= 2 # 2 #y= 22 #y


12 = 2 # 2 # 3 = 22 # 3 3 y= 3 #y


2

3 y

+

1

4 y

1

12

+

7

15

EXAMPLE 2
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