9.1 Multiplying and Dividing Rational Expressions

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.

Divide the same expression from numerator and denominator

97

732

yy

yy

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

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

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

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

Simplify

Assume the denominator cannot equal zero.

baa

aba33

44

2

2

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

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

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

Multiply the fractions

Reduce to simplest form

3

5

7

12

Multiply the fractions

Reduce to simplest form.

Multiply straight across

21

60

3

5

7

12

Multiply the fractions

Reduce to simplest form

7

20

3

3

21

60

3

5

7

12

Multiply the fractions

Reduce to simplest form.

7

20

1

5

7

4

7

20

3

3

21

60

3

5

7

12

herehappenedWhat

Multiply the fractions

Reduce before multiply.

3

2

3 16

7

21

8

x

y

y

x

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

Multiply the fractions

Reduce before multiply.

23

24

15

24

12

5

ba

bc

b

ca

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

Multiply the fractions

Reduce before multiply.

34

1

1

32

2

kk

k

k

k

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

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

What is the difference of Division and Multiply of fractions?

Do you remember?

4

3

7

2

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

Divide the Rational Expressions

You can only Reduce when Multiplying

222

2

6

5

3

10

dc

px

dc

px

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

Definition of Complex fraction

A fraction with fractions in the numerator or denominator.

7531

How to simplify a Complex fraction

Remember fractions are division statements.

15

7

5

7

3

1

7

5

3

1

7531

Simplify the Complex fraction

Remember fractions are division statements.

xyx

yxx

32

493

22

2

Simplify the Complex fraction

Remember fractions are division statements.

xy

x

yx

x

xyx

yxx

3249

32

49 3

22

2

3

22

2

Simplify the Complex fraction

322

23

22

2 32

493249 x

xy

yx

x

xy

x

yx

x

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

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

Homework

Page 476 – 477

# 15,19, 23,

27, 31, 35,

37, 41

Homework

Page 476 – 477

# 16,20, 24,

28, 32, 36,

38, 40