Adding Rational ExpressionsLesson 8C

Patrick White

April 21, 2009

Patrick White () Adding Rational Expressions April 21, 2009 1 / 18

Outline

1 Lesson 8C

2 Introduction

3 Adding with Like Denominators

4 Adding with Unlike Denominators

Patrick White () Adding Rational Expressions April 21, 2009 2 / 18

Objective

This unit is about rational expressions, which are like fractions. Last classwe learned how to multiply and simplify rational expressions. Today wewill learn to add and subtract them. In future classes, our adding andsubtracting problems will be more involved. Todays problems have all thesame steps as the hard problems. But the algebra is easier!

Homework

Please complete the even numbered problems on Worksheet 8C.Homework points will be given for correct answers only!

Patrick White () Adding Rational Expressions April 21, 2009 3 / 18

Objective

This unit is about rational expressions, which are like fractions. Last classwe learned how to multiply and simplify rational expressions. Today wewill learn to add and subtract them. In future classes, our adding andsubtracting problems will be more involved. Todays problems have all thesame steps as the hard problems. But the algebra is easier!

Homework

Please complete the even numbered problems on Worksheet 8C.Homework points will be given for correct answers only!

Patrick White () Adding Rational Expressions April 21, 2009 3 / 18

Outline

1 Lesson 8C

2 Introduction

3 Adding with Like Denominators

4 Adding with Unlike Denominators

Patrick White () Adding Rational Expressions April 21, 2009 4 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=

(3x + y) + (2x 7y)x2y

=5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

The LCM (least-common-multiple) of two numbers is the smallestnumber that is a multiple of both.

The LCM of 10 and 15 is 30.

The LCM of 5 and 7 is 35.

the LCM of 36 and 72 is 72.

The LCM of of 12 and 14 is 84.

To add rational expressions with like denominators, you simply add thenumerators, and keep the denominator.

3x + y

x2y+

2x 7yx2y

=(3x + y) + (2x 7y)

x2y=

5x 6yx2y

To add rational expressions with unlike denominators, you must first findthe LCM of the denominators, or the LCD (least common denominator).

3x

x2y2+

4x 1xy

=??

Patrick White () Adding Rational Expressions April 21, 2009 5 / 18

Outline

1 Lesson 8C

2 Introduction

3 Adding with Like Denominators

4 Adding with Unlike Denominators

Patrick White () Adding Rational Expressions April 21, 2009 6 / 18

Example 1

3x + 6y

x2y+

x + y

x2y=

=(3x + 6y) + (x + y)

x2y

=4x + 7y

x2y

Patrick White () Adding Rational Expressions April 21, 2009 7 / 18

Example 1

3x + 6y

x2y+

x + y

x2y=

=(3x + 6y) + (x + y)

x2y

=4x + 7y

x2y

Patrick White () Adding Rational Expressions April 21, 2009 7 / 18

Example 1

3x + 6y

x2y+

x + y

x2y=

=(3x + 6y) + (x + y)

x2y

=4x + 7y

x2y

Patrick White () Adding Rational Expressions April 21, 2009 7 / 18

Example 2

x 5y36xy

5x36xy

=(x 5y) (5x)

36xy

=4x 5y

36xy

Patrick White () Adding Rational Expressions April 21, 2009 8 / 18

Example 2

x 5y36xy

5x36xy

=(x 5y) (5x)

36xy

=4x 5y

36xy

Patrick White () Adding Rational Expressions April 21, 2009 8 / 18

Example 2

x 5y36xy

5x36xy

=(x 5y) (5x)

36xy

=4x 5y

36xy

Patrick White () Adding Rational Expressions April 21, 2009 8 / 18

Example 3

5x

24y3+

x + 3y

24y3

=5x + (x + 3y)

24y3

=6x + 3y

24y3

=3(2x + y)

24y3

=2x + y

8y3

Patrick White () Adding Rational Expressions April 21, 2009 9 / 18

Example 3

5x

24y3+

x + 3y

24y3

=5x + (x + 3y)

24y3

=6x + 3y

24y3

=3(2x + y)

24y3

=2x + y

8y3

Patrick White () Adding Rational Expressions April 21, 2009 9 / 18

Example 3

5x

24y3+

x + 3y

24y3

=5x + (x + 3y)

24y3

=6x + 3y

24y3

=3(2x + y)

24y3

=2x + y

8y3

Patrick White () Adding Rational Expressions April 21, 2009 9 / 18

Example 3

5x

24y3+

x + 3y

24y3

=5x + (x + 3y)

24y3

=6x + 3y

24y3

=3(2x + y)

24y3

=2x + y

8y3

Patrick White () Adding Rational Expressions April 21, 2009 9 / 18

Example 3

5x

24y3+

x + 3y

24y3

=5x + (x + 3y)

24y3

=6x + 3y

24y3

=3(2x + y)

24y3

=2x + y

8y3

Patrick White () Adding Rational Expressions April 21, 2009 9 / 18

Example 4

5a 6b25b2

6a25b2

=(5a 6b) (6a)

25b2

=a 6b

25b2

Patrick White () Adding Rational Expressions April 21, 2009 10 / 18

Example 4

5a 6b25b2

6a25b2

=(5a 6b) (6a)

25b2

=a 6b

25b2

Patrick White () Adding Rational Expressions April 21, 2009 10 / 18

Example 4

5a 6b25b2

6a25b2

=(5a 6b) (6a)

25b2

=a 6b

25b2

Patrick White () Adding Rational Expressions April 21, 2009 10 / 18

Example 5

x + 3y

30x3+

x y30x3

=(x + 3y) + (x y)

30x3

=2x + 2y

30x3

=2(x + y)

30x3

=x + y

15x3

Patrick White () Adding Rational Expressions April 21, 2009 11 / 18

Example 5

x + 3y

30x3+

x y30x3

=(x + 3y) + (x y)

30x3

=2x + 2y

30x3

=2(x + y)

30x3

=x + y

15x3

Patrick White () Adding Rational Expressions April 21, 2009 11 / 18

Example 5

x + 3y

30x3+

x y30x3

=(x + 3y) + (x y)

30x3

=2x + 2y

30x3

=2(x + y)

30x3

=x + y

15x3

Patrick White () Adding Rational Expressions April 21, 2009 11 / 18

Example 5

x + 3y

30x3+

x y30x3

=(x + 3y) + (x y)

30x3

=2x + 2y

30x3

=2(x + y)

30x3

=x + y

15x3

Patrick White () Adding Rational Expressions April 21, 2009 11 / 18

Example 5

x + 3y

30x3+

x y30x3

=(x + 3y) + (x y)

30x3

=2x + 2y

30x3

=2(x + y)

30x3

=x + y

15x3

Patrick White () Adding Rational Expressions April 21, 2009 11 / 18

Example 6

6x + y

10y x 6y

10y

=(6x + y) (x 6y)

10y

=5x + 7y

10y

Patrick White () Adding Rational Expressions April 21, 2009 12 / 18

Example 6

6x + y

10y x 6y

10y

=(6x + y) (x 6y)

10y

=5x + 7y

10y

Patrick White () Adding Rational Expressions April 21, 2009 12 / 18

Example 6

6x + y

10y x 6y

10y

=(6x + y) (x 6y)

10y

=5x + 7y

10y

Patrick White () Adding Rational Expressions April 21, 2009 12 / 18

Outline

1 Lesson 8C

2 Introduction

3 Adding with Like Denominators

4 Adding with Unlike Denominators

Patrick White () Adding Rational Expressions April 21, 2009 13 / 18

The Steps for Unlike Denominators

To add or subtract rational expressions, you must get the samedenominators first. If the denominators are different you must

1 Find the LCD (least common denominator)

2 Find what each denominator is missing from the LCD.

3 Multiply each fraction on top and bottom by what its denominator ismissing.

4 Add or subtract the numerators; denominator stays the same!

5 Simplify

Patrick White () Adding Rational Expressions April 21, 2009 14 / 18

Example 7

4x

5 5

6y

The LCD is

30y . Multiply each fraction by what the denominator ismissing!

4x

5 5

6y=

6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 7

4x

5 5

6y

The LCD is 30y .

Multiply each fraction by what the denominator ismissing!

4x

5 5

6y=

6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 7

4x

5 5

6y

The LCD is 30y . Multiply each fraction by what the denominator ismissing!

4x

5 5

6y=

6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 7

4x

5 5

6y

The LCD is 30y . Multiply each fraction by what the denominator ismissing!

4x

5 5

6y

=6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 7

4x

5 5

6y

The LCD is 30y . Multiply each fraction by what the denominator ismissing!

4x

5 5

6y=

6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 7

4x

5 5

6y

The LCD is 30y . Multiply each fraction by what the denominator ismissing!

4x

5 5

6y=

6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 7

4x

5 5

6y

The LCD is 30y . Multiply each fraction by what the denominator ismissing!

4x

5 5

6y=

6y

6y

4x

5 5

5

5

6y

=24xy

30y 25

30y

=24xy 25

30y

Patrick White () Adding Rational Expressions April 21, 2009 15 / 18

Example 8

y

2x 3

5y

The LCD is

6xy . Multiply each fraction by what the denominator ismissing!

y

2x 3

5y=

5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 8

y

2x 3

5y

The LCD is 6xy .

Multiply each fraction by what the denominator ismissing!

y

2x 3

5y=

5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 8

y

2x 3

5y

The LCD is 6xy . Multiply each fraction by what the denominator ismissing!

y

2x 3

5y=

5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 8

y

2x 3

5y

The LCD is 6xy . Multiply each fraction by what the denominator ismissing!

y

2x 3

5y

=5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 8

y

2x 3

5y

The LCD is 6xy . Multiply each fraction by what the denominator ismissing!

y

2x 3

5y=

5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 8

y

2x 3

5y

The LCD is 6xy . Multiply each fraction by what the denominator ismissing!

y

2x 3

5y=

5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 8

y

2x 3

5y

The LCD is 6xy . Multiply each fraction by what the denominator ismissing!

y

2x 3

5y=

5y

5y

y

2x 2x

2x

3

5y

=5y2

10xy 6x

10xy

=5y2 6x

10xy

Patrick White () Adding Rational Expressions April 21, 2009 16 / 18

Example 9

x

2y 3

8y

The LCD is

8y . Multiply each fraction by what the denominator is missing!

x

2y 3

8y=

4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

Example 9

x

2y 3

8y

The LCD is 8y .

Multiply each fraction by what the denominator is missing!

x

2y 3

8y=

4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

Example 9

x

2y 3

8y

The LCD is 8y . Multiply each fraction by what the denominator is missing!

x

2y 3

8y=

4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

Example 9

x

2y 3

8y

The LCD is 8y . Multiply each fraction by what the denominator is missing!

x

2y 3

8y

=4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

Example 9

x

2y 3

8y

The LCD is 8y . Multiply each fraction by what the denominator is missing!

x

2y 3

8y=

4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

Example 9

x

2y 3

8y

The LCD is 8y . Multiply each fraction by what the denominator is missing!

x

2y 3

8y=

4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

Example 9

x

2y 3

8y

The LCD is 8y . Multiply each fraction by what the denominator is missing!

x

2y 3

8y=

4

4

x

2y 1

1

3

8y

=4x

8y 3

8y

=4x 3

8y

Patrick White () Adding Rational Expressions April 21, 2009 17 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x?

15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x?

15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y?

6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y?

24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1?

x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z?

x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:

1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

LCM Practice

The hardest part in getting started with this lesson is often finding theLCD. So lets practice with some. What is the LCM of each of thefollowing?

1 5x and 3x? 15x

2 5 and 3x? 15x

3 3xy and 6x2y? 6x2y

4 8x and 12y? 24xy

5 x and 1? x

6 x2y2z and xy3z? x2y3z

Remember the rule:1 Find the LCM of the numbers first

2 Then take every variable, to the highest power each one appears.

Patrick White () Adding Rational Expressions April 21, 2009 18 / 18

Lesson 8CIntroductionAdding with Like DenominatorsAdding with Unlike Denominators