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9.2 Adding and 9.2 Adding and Subtracting Subtracting Rational Rational Expressions Expressions Least Common Denominator Least Common Denominator of a polynomial of a polynomial

9.2 Adding and Subtracting Rational Expressions

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9.2 Adding and Subtracting Rational Expressions. Least Common Denominator of a polynomial. Adding fractions. What do you need to add or subtract fractions? A common denominator Of 5 and 3, it is 5 times 3 = 15 (Since both are prime numbers) We multiply. Since both numbers divide into - PowerPoint PPT Presentation

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Page 1: 9.2 Adding and Subtracting Rational Expressions

9.2 Adding and 9.2 Adding and Subtracting Rational Subtracting Rational

ExpressionsExpressions

Least Common DenominatorLeast Common Denominator

of a polynomialof a polynomial

Page 2: 9.2 Adding and Subtracting Rational Expressions

Adding fractions What do you need to add or subtract

fractions?

A common denominator

Of 5 and 3, it is 5 times 3 = 15

(Since both are prime numbers)

We multiply.

Since both numbers divide into

15, it is the Least Common Multiply

3

2

5

1

15

13

15

10

15

3

15

10

5

5

3

215

3

3

3

5

1

Page 3: 9.2 Adding and Subtracting Rational Expressions

What is the L.C.M.

Given the terms

To find the LCM of the numbers, find there factor multiplication.

632532 20,16,15 caandcbbca

52220

222216

5315

Page 4: 9.2 Adding and Subtracting Rational Expressions

What is the L.C.M.

The LCM is the highest number of each factor listed from each number.

632532 20,16,15 caandcbbca

52220

222216

5315

240

222253

LCM

LCM

Page 5: 9.2 Adding and Subtracting Rational Expressions

What is the L.C.M.

The LCM is the highest number of each variable listed from each term.

632532 20,16,15 caandcbbca

63

25

32

20

16

15

ca

cb

bca653240 cbaLCM

Page 6: 9.2 Adding and Subtracting Rational Expressions

Find the LCM of two polynomial

Factor out the polynomial

44

2

2

23

xx

xxx

Page 7: 9.2 Adding and Subtracting Rational Expressions

Find the LCM of two polynomial

Factor out the polynomial

2244

12

22

2

223

xxxx

xxx

xxxxxx

Page 8: 9.2 Adding and Subtracting Rational Expressions

Find the LCM of two polynomial

Factor out the polynomial

2244

12

22

2

223

xxxx

xxx

xxxxxx

221

212

xxxLCM

xxxxLCM

Page 9: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

What is the LCM of 6 and 14

22

2

14

9

6

5

bab

a

42732

7214

326

LCM

Page 10: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

Common denominator 42a2b2

What does 6b times = 42a2b2

What does 14a2b2 times = 42a2b2

22

2

14

9

6

5

bab

a

Page 11: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

Common denominator 42a2b2

What does 6b times = 42a2b2

What does 14a2b2 times = 42a2b2

22

2

14

9

6

5

bab

a

Page 12: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

22

2

14

9

6

5

bab

a

22

2

22

14

9

7

7

6

5

ba

ba

ba

b

a

Page 13: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

22

2

14

9

6

5

bab

a

3

3

14

9

42

35

7

7

6

5

22

22

4

2

22

ba

ba

ba

ba

ba

b

a

Page 14: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

22

2

14

9

6

5

bab

a

2222

4

2222

22

4

2

22

42

27

42

35

42

27

3

3

14

9

42

35

7

7

6

5

baba

ba

baba

ba

ba

ba

ba

b

a

Page 15: 9.2 Adding and Subtracting Rational Expressions

Add the Rational Expressions

Simplify

22

2

14

9

6

5

bab

a

22

4

2222

4

2222

22

4

2

22

42

2735

42

27

42

35

42

27

3

3

14

9

42

35

7

7

6

5

ba

ba

baba

ba

baba

ba

ba

ba

ba

b

a

Page 16: 9.2 Adding and Subtracting Rational Expressions

What are the differences between Adding and Multiplying fractions

Simplify

306

153

153

10

x

x

x

x

Page 17: 9.2 Adding and Subtracting Rational Expressions

What are the differences between Adding and Multiplying fractions

Simplify

56

53

53

10

306

153

153

10

x

x

x

x

x

x

x

x

Page 18: 9.2 Adding and Subtracting Rational Expressions

What are the differences between Adding and Multiplying fractions

Simplify

56

53

532

102

56

53

53

10

306

153

153

10

x

x

x

x

x

x

x

x

x

x

x

x

Page 19: 9.2 Adding and Subtracting Rational Expressions

What are the differences between Adding and Multiplying fractions

Simplify

56

53102

56

53

532

102

56

53

53

10

306

153

153

10

x

xx

x

x

x

x

x

x

x

x

x

x

x

x

Page 20: 9.2 Adding and Subtracting Rational Expressions

What are the differences between Adding and Multiplying fractions

Simplify

56

153202

56

53102

56

53

532

102

56

53

53

10

306

153

153

10

x

xx

x

xx

x

x

x

x

x

x

x

x

x

x

x

x

Page 21: 9.2 Adding and Subtracting Rational Expressions

What are the differences between Adding and Multiplying fractions

Simplify

56

5

56

153202

56

53102

56

53

532

102

56

53

53

10

306

153

153

10

x

x

x

xx

x

xx

x

x

x

x

x

x

x

x

x

x

x

x

Page 22: 9.2 Adding and Subtracting Rational Expressions

The complex fraction

Simplify

11

11

b

ba

Page 23: 9.2 Adding and Subtracting Rational Expressions

The complex fraction

Simplify

11

11

b

ba

1

111

bba

Page 24: 9.2 Adding and Subtracting Rational Expressions

The complex fraction

Simplify

11

11

b

ba

b

b

bab

a

ab

b

bba

1

1111

Page 25: 9.2 Adding and Subtracting Rational Expressions

The complex fraction

Simplify

11

11

b

ba

b

b

ab

ba

b

b

bab

a

ab

b

bba

1

1

1111

Page 26: 9.2 Adding and Subtracting Rational Expressions

The complex fraction

Simplify

11

11

b

ba

b

b

ab

ba

b

b

ab

ba

b

b

bab

a

ab

b

bba

1

1

1

1111

Page 27: 9.2 Adding and Subtracting Rational Expressions

The complex fraction

Simplify

11

11

b

ba

ba

ba

ba

ba

b

b

ab

ba

b

b

ab

ba

b

b

bab

a

ab

b

bba

11

1

1

1

1

1111

Page 28: 9.2 Adding and Subtracting Rational Expressions

Homework Homework

Page 482 – 483Page 482 – 483

## 15, 19, 25, 29, 15, 19, 25, 29,

33, 37, 4133, 37, 41

Page 29: 9.2 Adding and Subtracting Rational Expressions

Homework

Page 482 – 483

# 16, 20, 24, 26,

28, 30, 34, 36