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Chapter 6 Section 4
Objectives
1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Adding and Subtracting Rational Expressions
Add rational expressions having the same denominator.
Add rational expressions having different denominators.
Subtract rational expressions.
6.4
2
3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 1
Add rational expressions having the same denominator.
Slide 6.4-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Add rational expressions having the same denominator.
Adding Rational Expressions (Same Denominator)
If and (Q ≠ 0) are rational expressions, then
ADD the numerators and keep the same denominator.
.P R P R
Q Q Q
P
Q
R
Q
Slide 6.4-4
2 2x y
x y x y
Add. Write each answer in lowest terms.
2 2x y
x y
2 x y
x y
2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 2
Add rational expressions having different denominators.
Slide 6.4-6
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Add rational expressions having different denominators.
Adding Rational Expressions (Different Denominators)
Step 1: Find the least common denominator (LCD).
Step 2: Rewrite each rational expression as an equivalent rational expression with the LCD as the denominator.
Step 3: Add the numerators to get the numerator of the sum. The LCD is the denominator of the sum.
Step 4: Write in lowest terms using the fundamental property.
Slide 6.4-7
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Add. Write each answer in lowest terms.
Solution:
2
3 7
m
n n
LCD 3 7 21n n
7 3
7
2
33 7
m
n n
7 6
21 21
m
n n 7 6
21
m
n
Slide 6.4-8
Adding Rational Expressions (Different Denominators)CLASSROOM EXAMPLE 2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:
2
2 4
1 1
p
p p
Add. Write the answer in lowest terms.
2 4
1 1 1
p
p p p
2 2
1 1
p
p p
2 4
1
1
11 1
p p
ppp p
2 2 4
1 1
p p
p p
12
11p
p
p
2
1p
Slide 6.4-9
Adding Rational ExpressionsCLASSROOM EXAMPLE 3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:
2 2
2 3
5 4 1
k
k k k
2 3
4 1 1 1
k
k k k k
Add. Write the answer in lowest terms.
1 4
1
2 3
4 1 41 1
k
k k k
k
kk
k
k
2 1 3 4
4 1 1 4 1 1
k k k
k k k k k k
22 2 3 12
4 1 1
k k k
k k k
22 5 12
4 1 1
k k
k k k
2 3 4
4 1 1
k k
k k k
Slide 6.4-10
Adding Rational ExpressionsCLASSROOM EXAMPLE 4
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Add. Write the answer in lowest terms.
Solution:
2 3 3 2
m n
m n n m
2 3 3 2
1
1
m n
m n n m
2 3 3 2
m n
m n n m
or 2 3 3 2
m n n m
m n n m
2 3 2 3
m n
m n m n
Slide 6.4-11
Adding Rational Expressions (Denominators Are Opposites)CLASSROOM EXAMPLE 5
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 3
Subtract rational expressions.
Slide 6.4-12
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
5 5
1 1
t t
t t
5 5
1
t t
t
5 5
1
t t
t
4 5
1
t
t
Solution:
Sign errors often occur in subtraction problems.
Be sure to use parentheses after the subtraction sign.
Slide 6.4-14
Subtracting Rational Expressions (Same Denominator)
Subtract. Write the answer in lowest terms.
CLASSROOM EXAMPLE 6
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
6 1
2 3a a
Subtract. Write the answer in lowest terms.
Solution:
36 1
2 3
2
3 2
a a
a aa a
6 18 2
2 3 3 2
a a
a a a a
6 18 2
2 3
a a
a a
6 18 2
2 3
a a
a a
5 20
2 3
a
a a
5 4
2 3
a
a a
Slide 6.4-15
Subtracting Rational Expressions (Different Denominators)CLASSROOM EXAMPLE 7
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
2 2
3 4
5 10 25
r
r r r r
Solution:
3 4
5 5 5
r
r r r r
3 4
55 5
5
5
rr
r r
r
r rr r
23 15 4
5 5 5 5
r r r
r r r r r r
23 19
5 5
r r
r r r
3 19
5 5
r
r
r
r r
2
3 19
5
r
r
Slide 6.4-17
Subtracting Rational Expressions
Subtract. Write the answer in lowest terms.
CLASSROOM EXAMPLE 9
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
4 3 1
1 1
x x
x x
Subtract. Write the answer in lowest terms.
Solution:
4 3 1
1 ( 11 )
x x
x x
4 3 1
1 1
x x
x x
4 3 1
1
x x
x
7 1
1
x
x
Slide 6.4-16
Subtracting Rational Expressions (Denominators Are Opposites)CLASSROOM EXAMPLE 8
4 3 1
1 ( 1)
x x
x x
