Do Now 5/29/09Do Now 5/29/09

Copy HW in your planner.Copy HW in your planner. Text p. 797, #4-38 evensText p. 797, #4-38 evens

Take out HW from last night.Take out HW from last night. Cumulative Test Cumulative Test

In your notebook, define and give two In your notebook, define and give two examples of examples of rational numbers.rational numbers. Text p. 762, #1-16 all, not 2Text p. 762, #1-16 all, not 2

HomeworkHomeworkText p. 762, #1-16 all; not 2Text p. 762, #1-16 all; not 2

1) 401) 40 3) 23) 2 4) -14) -1 5) (x – 5)(x + 3)5) (x – 5)(x + 3) 6) 2(x – 3)(x – 1)6) 2(x – 3)(x – 1) 7) (3x + 5)(3x – 5)7) (3x + 5)(3x – 5) 8) 3x(x + 4)(x – 4)8) 3x(x + 4)(x – 4) 9) 1 1/129) 1 1/12

10) 19/4010) 19/40 11) 1/311) 1/3 12) 1 1/412) 1 1/4 13) 9/413) 9/4 14) 614) 6 15) -3, 215) -3, 2 16) 1316) 13

ObjectiveObjectiveSWBAT simplify rational expressions.SWBAT simplify rational expressions.

Section 12.4 Section 12.4 “Simplify Rational Expressions”“Simplify Rational Expressions”

A A RATIONAL EXPRESSIONRATIONAL EXPRESSION is an is an expression that can be written as a ratio (fraction) expression that can be written as a ratio (fraction) of two polynomials where the denominator is not 0.of two polynomials where the denominator is not 0.

A rational expression is A rational expression is UNDEFINEDUNDEFINED when the when the denominator is equal to 0. denominator is equal to 0.

A number that makes a rational expression undefined is A number that makes a rational expression undefined is called an called an EXCLUDED VALUEEXCLUDED VALUE. .

3

2

x 58

272

ww

w

Find the excluded values, if any, of the expression. Find the excluded values, if any, of the expression.

0x

x

x

10

8

EXAMPLE 1EXAMPLE 1

142

5

y

7y

9

42 v

v

)3)(3(92 vvv

58

72 ww

w

16

1591 x3,3 v

FactorFactor

Use quadratic Use quadratic formula to find formula to find when w = 0.when w = 0.

a

acbbx

2

42

)8(2

)5)(8(411 2 x

There are no excluded values

Simplify Rational ExpressionsSimplify Rational Expressions

To simplify a rational expression, you can To simplify a rational expression, you can factor the numerator and denominator and factor the numerator and denominator and then divide out any common factors. then divide out any common factors.

A rational expression is in A rational expression is in SIMPLEST FORMSIMPLEST FORM if the numerator and denominator have no if the numerator and denominator have no factors in common other than 1. factors in common other than 1.

34

12

x

xxxx

x

4

342

3

x

Simplify the rational expression, if possible. State the Simplify the rational expression, if possible. State the excluded values. excluded values.

0a

6

3

22

4

a

a

EXAMPLE 2EXAMPLE 2

5

2

cc

5c

2

23

18

126

m

mm

)3(6

)2(62

2

m

mm

0m

FactorFactor

311

2

a 5

2

cc

3

2m

Simplify the rational expression, if possible. State the Simplify the rational expression, if possible. State the excluded values. excluded values.

2,4 x

86

1032

2

xx

xx

EXAMPLE 3EXAMPLE 3

)2)(4( xxFactorFactor )2)(5( xx

4

5

x

x

2,5 x

107

232

2

xx

xx)5)(2( xx

FactorFactor )2)(1( xx

5

1

x

x

Simplify the rational expression, if possible. State the Simplify the rational expression, if possible. State the excluded values. excluded values.

4,4x

2

2

16

127

x

xx

EXAMPLE 4EXAMPLE 4

)4)(4( xx

FactorFactor

)4)(3( xx

x

x

4

3

Recognize opposites

Recognize Recognize oppositesopposites

)4)(4(

)4)(3(

xx

xx

Multiply by -1Multiply by -1Rewrite (4-x) as -(x-4)Rewrite (4-x) as -(x-4)

2,5 x

103

452

2

zz

zz)2)(5( zz

FactorFactor

)1)(5( zz

2

1

z

z

Recognize Recognize oppositesopposites

)2)(5(

)1)(5(

zz

zz

Multiply by -1Multiply by -1Rewrite (z-5) as -(z+5)Rewrite (z-5) as -(z+5)

Classwork/HomeworkClasswork/Homework

Text p. 797, #4-36 multiples of 4Text p. 797, #4-36 multiples of 4

HomeworkHomework Practice worksheet 12.4 evensPractice worksheet 12.4 evens

3

7x

2,6x

3,7;7

1

x

x

x2

12x

6)6)

8)8)

14)14)

16)16)4)4)

)1(

23

xx

x18)18)

5x2)2)

0;2 xx

3;4 x

10)10)

12)12)