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8.5 Rational Expressions with Like Denominators

CORD Math

Mrs. Spitz

Fall 2006

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Objective

• Add and subtract rational expressions with like denominators.

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Upcoming

• 8.5 Tuesday/Wednesday – Skip 8.6

• 8.7 Thursday 10/26

• 8.8 Friday 10/27

• 8.9 Monday 10/30

• 8.10 Tuesday/Wed

• Chapter 8 Review Wed/Thur

• Chapter 8 Test Friday

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Assignment

• Pg. 324 #4-41 all

• Midchapter Review pg. 325 #1-11

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Introduction

• To add or subtract fractions with like denominators, you add or subtract the numerators. Then you write the sum or difference over the common denominator.

7

5

7

2

7

3

9

5

9

2

9

7

You can use these same methods to add or subtract rational expressions.

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Ex. 1: Find .2

1

2

3

xx

2

13

2

1

2

3

xxx

2

4

x

Since x + 2 is the common denominator, add the numerators.

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Ex. 2: Find .7

3

7

23

a

a

a

a

7

)]3([)23(

7

3

7

23

a

aa

a

a

a

a

7

323

a

aa

Add the additive inverse of a - 3.

7

52

a

a

Distributive Property

Remember when subtracting rational expressions to add the additive inverse of the second expression.

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Express in simplest form.

• When adding or subtracting fraction, sometimes the result can be expressed in simplest form.

2

1

8

4

8

1

8

3

The GCF of 4 and 8 is 4.

8

3

16

6

16

3

16

9

The GCF of 6 and 16 is 2.

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Ex. 3: Find .43

52

43

38

n

n

n

n

43

)52()38(

43

52

43

38

n

nn

n

n

n

n

43

5238

n

nn

Since 3n+4 is the common denominator, subtract the numerators.

)43(

)43(2

n

n

Combine like terms.

2

Factor out a 2 out of the numerator and cancel 3n+4 from both numerator and denominator.

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Ex. 4: Find .2

1

2 x

x

x

x

)2(

1

22

1

2

x

x

x

x

x

x

x

x

)2

1(

2

x

x

x

x

Rewrite 2 – x as x – 2 by multiplying by -1.

2

12

1

2

x

xxx

x

x

x

Remember

2

12

x

x

Simplify and combine like terms.

xx

11

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Example 5: Application

• Find the measure of the perimeter of the rectangle.

22 sr

r

22 sr

s

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Ex. 5: Find the measure of the perimeter of the rectangle.

wlP 22 )(2)(2

2222 sr

s

sr

r

2222

22

sr

s

sr

r

22

22

sr

sr

))((

)(2

srsr

sr

sr

2

sr

2

← Perimeter formula for rectangle.

← Substitute values.

← Distributive Property

← Combine like terms

← Factor out 2 as common factor and cancel terms that are same in numerator and denominator.

22 sr

r

22 sr

s

The measure of the perimeter is:

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Upcoming

• Midchapter Quiz – 20 points apiece so I can see how you are doing.

• Skipping 8.6• 8.7 Rational expression with Unlike Denominators.• 8.8 Mixed expressions and complex fractions.• 8.9 Solving Rational Equations• 8.10 Application: Formulas. • Chapter 8 Review• Chapter 8 Exam• Binder Check. Make sure you have all notes from

each section, or download off the web. You must recopy to get full credit.