Chapter 7 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiplying...

Chapter 7 Section 2

Objectives

1

Copyright © 2012, 2008, 2004 Pearson Education, Inc.

Multiplying and Dividing Rational Expressions

Multiply rational expressions.

Divide rational expressions.

7.2

2


Objective 1


Slide 7.2-3



Multiplying Rational Expressions

The product of the rational expressions and is

That is, to multiply rational expressions, multiply the numerators and multiply the denominators.

P

QR

SP R PR

Q S QS

Slide 7.2-4

The product of two fractions is found by multiplying the numerators and multiplying the denominators. Rational expressions are multiplied in the same way.


Multiply. Write each answer in lowest terms.

Solution:

2 5

7 10

2

2

8 9

3

p q

pq

2 5

7 10

2

2

8 9

3

p q

p q

7

2 5

2 5

1

7

38

3

3p qp

p q q

24p

q

It is also possible to divide out common factors in the numerator and denominator before multiplying the rational expressions.

Slide 7.2-5

EXAMPLE 1 Multiplying Rational Expressions


Multiply. Write the answer in lowest terms.

Solution:

3

2

p q q

p p q

3

2

p q q

p q p

3

2

q

q p

p q

p

3

2

q

p

Slide 7.2-6



Multiply. Write the answer in lowest terms.

2

2

7 10 6 6

3 6 2 15

x x x

x x x

Solution:

2

2

7 10 6 6

3 6 2 15

x x x

x x x

2 13 2

3 5 3

5

2

x x x

xx x

2 1

3

x

x

2 6 6

3 3

5

56

x x

x

x

x x

Slide 7.2-7



Objective 2


Slide 7.2-8



Dividing Rational Expressions

If and are any two rational expressions with then

That is, to divide one rational expression by another rational expression, multiply the first rational expression by the reciprocal of the second rational expression.

.P R P S PS

Q S Q R QR

0,R

S

R

S

P

Q

Slide 7.2-9


Solution:

4

3 44

5

3 16

4 5 12

5

3

2

3

3

p p

pp p

3 5

4 16

2

3

3 4

3 4

9

6

p p

p p

Divide. Write each answer in lowest terms.

2 39 6

3 4 3 4

p p

p p

3

2p

Slide 7.2-10

EXAMPLE 4 Dividing Rational Expressions


Divide. Write the answer in lowest terms.

Solution:

2 25 10

2 8

a b ab

2

2

5 8

2 10

a b

ab 5 2 2

2 2 5

2a b

a

a

bb

2a

b

Slide 7.2-11



Divide. Write the answer in lowest terms.

2

2

4 3 3

2 1 4 1

x x x x

x x

2

2

4 4

1

3

2 3

1xx x

x x x

2 1

1

4 2

2

1

1

x x

xx

x

x

4 2 1x

x

Solution:

Slide 7.2-12



2

2 21 2 1

ab a a b

a a a

Divide. Write in the answer in lowest terms.

Solution:

1 1

1

1

1

a aa b a

a ba a

2 2

2

2 1

1

ab a a a

a a b

1

1

a a

a

Remember to write −1 when dividing out factors that are opposite of each other. It may be written in the numerator or denominator, but not both.

Slide 7.2-13

EXAMPLE 7 Dividing Rational Expressions (Factors Are Opposites)


Multiplying or Dividing Rational Expressions.

Multiplying or Dividing Rational Expressions

Step 1: Note the operation. If the operation is division, use the definition of division to rewrite it as multiplication.

Step 2: Multiply numerators and denominators.

Step 3: Factor all numerators and denominators completely.

Step 4: Write in lowest terms using the fundamental property.

Step 2 and Step 3 may be interchanged based on personal preference.

Slide 7.2-14


HL 7.2Book Beginning AlgebraPage 433 Exercises 11,12,13,14,23,24,25,26,28,29,34,35,36,37,38.

Chapter 7 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiplying...

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Transcript of Chapter 7 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiplying...