Simplifying4 3

5 5

x x

x

2

5

25

q

q

3x

3

5

x

5q

1

5q

1x

5 1x 5q 5q

5.1 – Basic Prop. & Reducing to Lowest Terms

Simplifying2

2

11 18

2

x x

x x

2x

9

1

x

x

9x

2x 1x

5.1 – Basic Prop. & Reducing to Lowest Terms

Simplifying4

4

x

x

4x

4x

4x

1 4x 1

5.1 – Basic Prop. & Reducing to Lowest Terms

3 2

3

5 2

3 15

a b

b a

10

2

3a 2b45 a 3b

2a9 b

Multiplication:

5.2 – Multiplication & Division of Rational Expressions

3 2

3

5 2

3 15

a b

b a

2 2a9 b

Multiplication: 1

3

2

1

5.2 – Multiplication & Division of Rational Expressions

Multiplication: 2

3 2

3 6 7

14 2

x x

x x

3

21

2x 2x

27x14 2x

1432

5.2 – Multiplication & Division of Rational Expressions

19

253

147

842

2

2

x

xx

xx

x

4 2x

7x 2x 3 1x

3 1x 3 1x 2x

4 2x

7x 3 1x

Multiplication:

5.2 – Multiplication & Division of Rational Expressions

y

xx

26

7 2

27

6

x 1

3

7xy

2y

x

1

3

Division:

5.2 – Multiplication & Division of Rational Expressions

2

123

6

4 2

xx

24

6

x

24

6

x

4

3

x 9

4x

2

3 12x

23 4x

1

1

3

1

3

Division:

5.2 – Multiplication & Division of Rational Expressions

2

25

4

410 23

2

x

xx

x

x

2

2

10 4

4

x

x

2

2x 2

22 xx

3 2

2

5 2

x

x x

5 2x

2x 2x 2x

2x 5 2x

2

1

x

Division:

5.2 – Multiplication & Division of Rational Expressions

21

129

147

8103 2

x

x

xx

21

21

23 10 8

7 14

x x

x

2x

1

7

21

9 12x

3 4x

7 2x 21

3 3 4x

21

31

Division:

5.2 – Multiplication & Division of Rational Expressions

6

5

3

2and

What is the Lowest Common Denominator (LCD)?

2

1

7

2,

4

3and

3 5

5 13and

x x4 2

17 3

4 6and

y y

6 28

5x 12 4y

5.3 – Addition & Subtraction of Rational Expressions

5

7

5

3

a

aand

a

a

What is the Lowest Common Denominator (LCD)?

123

5

4

72

2

x

xand

x

x

5a

3

27xand 5x

4x 4x

243 x

4x 4x 3 4x 5a

5.3 – Addition & Subtraction of Rational Expressions

23

3

32

522

yy

yand

yy

y

What is the Lowest Common Denominator (LCD)?

1y

5y

3y 2y

3y 1y and

3y

1y 2y

5.3 – Addition & Subtraction of Rational Expressions

73

7

73

3

xx

x

Examples (Like Denominators):

1

3 7x 3x 7

5.3 – Addition & Subtraction of Rational Expressions

2

64

2

52 2

x

x

x

xx

Examples (Like Denominators):

2x 22 5

2

x x

x

22

2

x

x

2x

32 x22 5x x 4 6x

4x 6

x 6

2x 2 3x

5.3 – Addition & Subtraction of Rational Expressions

65

72

65

1322

xx

x

xx

x

Examples (Like Denominators):

65

72132

xx

xx

65

132

xx

x x2 7

65

62

xx

x

6x

x 1 x 6

1

1

x

1

1

5.3 – Addition & Subtraction of Rational Expressions

Examples:

15

3

5

yy

LCD 15

15

3

5

yy

3

3

15

3

15

3 yy

15

33 yy 15

00

5.3 – Addition & Subtraction of Rational Expressions

Examples:

210

11

8

5

xx

LCD 40x2

210

11

8

5

xx

x

x

5

5

22 40

44

40

25

xx

x 240

4425x

x

4

4

5.3 – Addition & Subtraction of Rational Expressions

Examples:

1

2

7

5

xx

LCD

5 2

7 1x x

7 1 7 1x x x x

7 1x x

7x 1x

1

1

x

x

7

7

x

x

5x 5 14x 19x 5

5.3 – Addition & Subtraction of Rational Expressions

3

5

9

102

xx

xExamples:

10x

10 5

3 3 3

x

x x x

10

3 3

x

x x

3 3x x

3 3x x

3 3x x

3

5

x

3x 3x

LCD

3

3

x

x

3 3x x 5x 15

10x 155x

5x 15

5 3x 3x 3x

5

3x

5.3 – Addition & Subtraction of Rational Expressions

812

3

23

42

x

x

xx

Examples:

LCD

4

4 3

3 2 4 3 2

x

x x x

x 3 2x 3x

4 3 2x

4 x 3 2x

4

4

x

x

5.3 – Addition & Subtraction of Rational Expressions

Examples: continued

4 3 2 4 3 2x x x x

4 3 2x x

x

x

x

x

xx 234

3

23

4

4

4

16 23x

216 3x

5.3 – Addition & Subtraction of Rational Expressions

444

622

x

x

xx

xExamples:

6x x

LCD

6

2 2 2 2

x x

x x x x

2x 2x 2x 2x

2x 2x 2x

2

2

x

x

2

2

x

x

5.3 – Addition & Subtraction of Rational Expressions

Examples: continued

2

2

2222

6

2

2

x

x

xx

x

xx

x

x

x

2 2 2 2 2 2x x x x x x

222

2126 22

xxx

xxxx

2 2 2x x x 22 2x x

26x 12x2x 2x

27x 10x x 7x 10

5.3 – Addition & Subtraction of Rational Expressions