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
- (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