mba10_ppt_0704.ppt1234567890111231399392

Add or subtract RAE

1. Chapter 7Chapter 7
Section 4Section 4
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Adding and Subtracting Rational
Expressions
Add rational expressions having the same
denominator.
Add rational expressions having different
denominators.
Subtract rational expressions.
1
3
2
7.47.4

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 11
Add rational expressions having
the same denominator.
Slide 7.4 - 3

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Add rational expressions having the same
denominator.
We find the sum of two rational expressions with the same
procedure that we used in Section 1.1 for adding two fractions
having the same denominator.
Slide 7.4 - 4
If and (Q ≠ 0) are rational expressions, then

That is, to add rational expressions with the same denominator,
add the numerators and keep the same denominator.
.
P R P R
Q Q Q

 
P
Q
R
Q

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 1
Add. Write each answer in lowest terms.
Solution:
Adding Rational Expressions
with the Same Denominator
Slide 7.4 - 5
7 3
15 15

2 2x y
x y x y

 
7 3
15


10
15

5
2
3
5


2
3

2 2x y
x y



2x y
x y



2

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 22
Add rational expressions having
different denominators.
Slide 7.4 - 6

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
We use the following steps, which are the same as those
used in Section 1.1 to add fractions having different
denominators.
Add rational expressions having different
denominators.
Slide 7.4 - 7
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.

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Add. Write each answer in lowest terms.
EXAMPLE 2
Solution:
Adding Rational Expressions
with Different Denominators
Slide 7.4 - 8
1 1
10 15

2
3 7
m
n n

1052 
LCD 3 7 21n n   
1553 
LCD 2 3 5 30   
3 2
30 2
1 1
1 15
  
3 2
30 30
 
5
30

1
6

7 3
7
2
33 7
m
n n
  
7 6
21 21
m
n n
 
7 6
21
m
n


3 2
30



9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 3
Solution:
2
2 4
1 1
p
p p


 
Adding Rational Expressions
Slide 7.4 - 9
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



10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 4
Solution:
2 2
2 3
5 4 1
k
k k k

  

2 3
4 1 1 1
k
k k k k
 
   
Adding Rational Expressions
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
 
 
      
2
2 2 3 12
4 1 1
k k k
k k k
  

  

2
2 5 12
4 1 1
k k
k k k
 

  
 

2 3 4
4 1 1
k k
k k k
 

  
Slide 7.4 - 10

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 5
Add. Write the answer in lowest terms.
Solution:
2 3 3 2
m n
m n n m

 
Adding Rational Expressions
with Denominators That Are
Opposites
Slide 7.4 - 11

2 3 3 2
1
1
m n
m n n m
  
 

 2 3 3 2
m n
m n n m

 
  
2 3
m n
m n


2 3 2 3
m n
m n m n

 
 

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 33
Slide 7.4 - 12
Subtract rational expressions.

13. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
We subtract rational expressions having different
denominators using a procedure similar to the one used to
add rational expressions having different denominators.
Subtract rational expressions.
Slide 7.4 - 13
If and (Q ≠ 0) are rational expressions, then
That is, to subtract rational expressions with the same
denominator, subtract the numerators and keep the same denominator.
P R P R
Q Q Q

 
R
Q
R
Q
Use the following rule to subtract rational expressions
having the same denominator.

14. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Subtract. Write the answer in lowest terms.
EXAMPLE 6
5 5
1 1
t t
t t


 
Subtracting Rational
Expressions with the Same
Denominator
Slide 7.4 - 14
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. The numerator of
the fraction being subtracted must be treated as a single quantity.
Be sure to use parentheses after the subtraction sign.

15. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 7
6 1
2 3a a

 
Subtracting Rational
Expressions with Different
Denominators
Slide 7.4 - 15
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


 

16. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 8
4 3 1
1 1
x x
x x
 

 
Subtracting Rational
Expressions with Denominators
That Are Opposite
Slide 7.4 - 16
Subtract. Write the answer in lowest terms.
Solution:
4 3 1
1 1
x x
x x

 
 


14 3 1
1 1 1
x x
x x
 
 




 4 3 1
1
x x
x
 


4 3 1
1
x x
x
 


1
1
x
x



1

17. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Subtract. Write the answer in lowest terms.

EXAMPLE 9
2 2
3 4
5 10 25
r
r r r r

  
Subtracting Rational
Expressions
Slide 7.4 - 17
Solution:

3 4
5 5 5
r
r r r r
 
    
3 4
55 5
5
5
rr
r r
r
r rr r


   
  

2
3 15 4
5 5 5 5
r r r
r r r r r r

 
   

2
3 19
5 5
r r
r r r


 
 

3 19
5 5
r
r
r
r r


 
 

2
3 19
5
r
r


