Chapter 6 Section 4 Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions.

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


Objective 1


Slide 6.4-3



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


Objective 2


Slide 6.4-6



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


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


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


Solution:

2 2

2 3

5 4 1

k

k k k

2 3

4 1 1 1

k

k k k k


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



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


Objective 3

Subtract rational expressions.

Slide 6.4-12


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


6 1

2 3a a


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


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


CLASSROOM EXAMPLE 9


4 3 1

1 1

x x

x x


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

Chapter 6 Section 4 Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions.

Documents

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rational expressionssubtract

lowest terms

equivalent rational

oppositesclassroom example

common denominator lcd

subtraction sign

sign errors