9.1 multiplying and dividing rational expressions

36
9.1 Multiplying and Dividing Rational Expressions Complex fractions

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9.1 Multiplying and Dividing Rational Expressions. Complex fractions. Definition of a Rational Expression. In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Since they are fractions. Simplify a Rational Expression. - PowerPoint PPT Presentation

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Page 1: 9.1 Multiplying and Dividing Rational Expressions

9.1 Multiplying and Dividing Rational Expressions

Complex fractions

Page 2: 9.1 Multiplying and Dividing Rational Expressions

Definition of a Rational Expression

In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions.

Page 3: 9.1 Multiplying and Dividing Rational Expressions

Since they are fractions

Simplify a Rational Expression.

Divide the same expression from numerator and denominator

97

732

yy

yy

Page 4: 9.1 Multiplying and Dividing Rational Expressions

Since they are fractions

Simplify a Rational Expression.

Divide the same expression from numerator and denominator

97

732

yy

yy

9

3

97

7322

y

y

yy

yy

Page 5: 9.1 Multiplying and Dividing Rational Expressions

Since they are fractions

There are numbers that will not work in the Rational expression.

They are -7, 3 and -3. Why?

9

3

97

7322

y

y

yy

yy

Page 6: 9.1 Multiplying and Dividing Rational Expressions

Since they are fractions

Factor out the denominator.

Can you see why -7, 3 and -3 do not work as answers?

337

73

yyy

yy

Page 7: 9.1 Multiplying and Dividing Rational Expressions

Since they are fractions

Factor out the denominator.

-7, 3 and -3 do not work as answersbecause they make the denominator zero.

They are called Excluded Values.

337

73

yyy

yy

Page 8: 9.1 Multiplying and Dividing Rational Expressions

Simplify

Assume the denominator cannot equal zero.

baa

aba33

44

2

2

Page 9: 9.1 Multiplying and Dividing Rational Expressions

Simplify

Assume the denominator cannot equal zero.

Factor out a negative one to move things around

ba

ba

baa

aba

2

2

2

23

4

33

44

Page 10: 9.1 Multiplying and Dividing Rational Expressions

Simplify

Assume the denominator cannot equal zero.

ba

ba

ba

ba

baa

aba

2

2

2

2

2

2

3

4

3

4

33

44

Page 11: 9.1 Multiplying and Dividing Rational Expressions

Simplify

Assume the denominator cannot equal zero.

a

a

a

ba

ba

ba

ba

baa

aba

3

4

3

4

3

4

33

44

2

2

2

2

2

2

Page 12: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce to simplest form

3

5

7

12

Page 13: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce to simplest form.

Multiply straight across

21

60

3

5

7

12

Page 14: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce to simplest form

7

20

3

3

21

60

3

5

7

12

Page 15: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce to simplest form.

7

20

1

5

7

4

7

20

3

3

21

60

3

5

7

12

herehappenedWhat

Page 16: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

3

2

3 16

7

21

8

x

y

y

x

Page 17: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

yxxy

x

y

y

x

22

3

2

3

6

1

2

1

3

1

16

7

21

8

Page 18: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

23

24

15

24

12

5

ba

bc

b

ca

Page 19: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

2

3

2

2

23

24

3

2

3

2

1

15

24

12

5

b

ac

b

cac

ba

bc

b

ca

Page 20: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

34

1

1

32

2

kk

k

k

k

Page 21: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

13

1

1

3

34

1

1

3

2

2

2

kk

k

k

k

kk

k

k

k

Page 22: 9.1 Multiplying and Dividing Rational Expressions

Multiply the fractions

Reduce before multiply.

1

1

1

1

1

13

111

1

3

13

1

1

3

34

1

1

3

2

2

2

kk

kk

k

k

kk

k

k

k

kk

k

k

k

Page 23: 9.1 Multiplying and Dividing Rational Expressions

What is the difference of Division and Multiply of fractions?

Do you remember?

4

3

7

2

Page 24: 9.1 Multiplying and Dividing Rational Expressions

What is the difference of Division and Multiply of fractions?

When dividing you multiply by the inverse of the second fraction.

21

8

3

4

7

2

4

3

7

2

Page 25: 9.1 Multiplying and Dividing Rational Expressions

Divide the Rational Expressions

You can only Reduce when Multiplying

222

2

6

5

3

10

dc

px

dc

px

Page 26: 9.1 Multiplying and Dividing Rational Expressions

Divide the Rational Expressions

You can only Reduce when Multiplying

dxdx

px

dc

dc

px

dc

px

dc

px

41

2

1

2

5

6

3

10

6

5

3

10

22

2

2

222

2

Page 27: 9.1 Multiplying and Dividing Rational Expressions

Definition of Complex fraction

A fraction with fractions in the numerator or denominator.

7531

Page 28: 9.1 Multiplying and Dividing Rational Expressions

How to simplify a Complex fraction

Remember fractions are division statements.

15

7

5

7

3

1

7

5

3

1

7531

Page 29: 9.1 Multiplying and Dividing Rational Expressions

Simplify the Complex fraction

Remember fractions are division statements.

xyx

yxx

32

493

22

2

Page 30: 9.1 Multiplying and Dividing Rational Expressions

Simplify the Complex fraction

Remember fractions are division statements.

xy

x

yx

x

xyx

yxx

3249

32

49 3

22

2

3

22

2

Page 31: 9.1 Multiplying and Dividing Rational Expressions

Simplify the Complex fraction

322

23

22

2 32

493249 x

xy

yx

x

xy

x

yx

x

Page 32: 9.1 Multiplying and Dividing Rational Expressions

Simplify the Complex fraction

322

23

22

2 32

493249 x

xy

yx

x

xy

x

yx

x

3

2 231

2323 x

yx

yxyx

x

Page 33: 9.1 Multiplying and Dividing Rational Expressions

Simplify the Complex fraction

322

23

22

2 32

493249 x

xy

yx

x

xy

x

yx

x

3

2 231

2323 x

yx

yxyx

x

yxxxyx 23

11

23

1

Page 34: 9.1 Multiplying and Dividing Rational Expressions
Page 35: 9.1 Multiplying and Dividing Rational Expressions

Homework

Page 476 – 477

# 15,19, 23,

27, 31, 35,

37, 41

Page 36: 9.1 Multiplying and Dividing Rational Expressions

Homework

Page 476 – 477

# 16,20, 24,

28, 32, 36,

38, 40