MS Algebra Ch. 11.2 Simplifying Rational...

MS Algebra – Ch. 11.2 Simplifying Rational Expressions

Mr. Deyo

By the end of the period, I will simplify rational expressions and determine their excluded values.

I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Learning Target

Title: 11.2 Simplifying Rational Expressions Date:

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?

2) Section 11.2 Pg. 691-692 3) Section ______

TxtBk. Problems #3-9 Odd Notes Copied on blank sheet #13-23 Odd

Solved and Put in Binder? of paper in Binder?

Table of ContentsDate Description Date Due

Storm Check (Think, Write, Discuss, Report)

Questions on which to ponder and answer:1. How are the two images similar?

2. How are they different?

3. How can these two images be related to math?

1) Rational Expression

2) Excluded Value

3) Simplest Form

4) Factors

Vocabulary

DAY 3 and/or DAY 4

1. Review the word

Friendly Definition

Physical Representation

2. Show how the word works

Synonyms/antonym

Word Problems

Related words/phrases

Example/non-example

Friendly DefinitionSketch

Wordwork Sentence

DAY 2

1. Review word

Friendly Definition


2. Draw a sketch

DAY 5

1. Review the word

Friendly definition


3. Write a sentence

at least 2 rich words (1 action)

correct spelling

correct punctuation

correct subject/predicate agreement

clear and clean writing

DAY 1

1. Use Visuals

2. Introduce the word

Friendly Definition


3. Use Cognates

4. Write friendly definition

5. Physical Representation

Word List1.2.3.4.

For use with pages xxx–xxxDaily Warm-Up Exercises

Factor the polynomial.

8x+x2 15+ –15x+2x2 8

For use with pages xxx–xxxDaily Warm-Up Exercises

Factor the polynomial.

( )8+x ( )12x –

8x+x2 15+

( )3+x ( )5+x

ANSWER ANSWER

–15x+2x2 8

Notes:

A number that makes a rational expression

undefined is called an excluded value.(makes the Denominator = 0)

A rational expression is in simplest formif the numerator and denominator have no factors in common other than 1.

Problem(s) A Find excluded values

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

10x

8+x+145

2ya. b.

Problem(s) A Find excluded values


10x

8+x+145

2y

SOLUTION

The expression is undefined when 10x = 0 or x = 0. The excluded

value is 0.

a. b.

The expression is undefined when 2y + 14 = 0 or y = -7. The

excluded value is -7.

a.

b.

Problem(s) B Find excluded values


c.

9

4v

v 2 – +5

2+7w

w+8w 2

d.

Problem(s) B Find excluded values


c.

9

4v

v 2 – +5

2+7w

w+8w 2

d.

The excluded values is -3 and 3.

There are no excluded values.

c.

d.

SOLUTION

Guided Practice


6n –

125n2n 2 – – m 2

2m

– 4

Guided Practice


6n –

125n2n 2 – – m 2

2m

– 4

, 42

3– 2–2,

ANSWERANSWER


Why are excluded values important when simplifying rational expressions?

Excluded values are important when simplifying

rational expressions because _______________

_______________________________________

_______________________________________.



Learning Target




TxtBk. Problems #4-10 Even Notes Copied on blank sheet #14-24 Even

Solved and Put in Binder? of paper in Binder?



2) Excluded Value

3) Simplest Form

4) Factors

Vocabulary

Problem(s) A Simplify expressions by dividing out monomials

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

a.

2rr b. 5x

( )2+x5 18m 2

12m 26m 3c. –

Problem(s) A Simplify expressions by dividing out monomials


a.

2rr b. 5x

( )2+x5 18m 2

12m 26m 3c. –

=2

1

SOLUTION

2r

ra. =

2r

r

The excluded value is 0.

The excluded value is – 2.

=2+x

x

b.5x

( )2+x5=

5

( )2+x5

x

•

•

=6m2 ( )2m

m236 • •

–

The excluded value is 0.

=2m –

3

=6m2 ( )2m –

m236 • •c.

Problem(s) B


22a 6

4a 3

c2c+ 5

Problem(s) B


22a 6

4a 3

c2c+ 5

11a 3

2; 0 c

2c+ 5

; – 5

ANSWERANSWER

Guided Practice


8s+2s 2

123s + 8x 3

8x

+ 16x 2

Guided Practice


8s+2s 2

123s + 8x 3

8x

+ 16x 2

; 432s – – 2;x 2

1+ 2x 0,

ANSWERANSWER


How can you tell if you have arrived at the simplest form of your rational expression?

I have arrived at the simplest form of my

rational expression when __________________

_______________________________________

_______________________________________.



Learning Target




TxtBk. Problems ________ Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?



2) Excluded Value

3) Simplest Form

4) Factors

Vocabulary

Standard Review

Simplify to lowest terms.

2(x + 5)

3x + 1

Multiple Choice Practice

1–9x 232x+6x 2 10+

2(x + 5)

3x – 1

2(3x + 5)

3x – 1

2(x + 1)

9(x – 1)

Standard Review

Divide out common factor.=2(x + 5)

(3x – 1) (3x + 1)

(3x + 1)

Simplify.=2(x + 5)

3x – 1

ANSWER The correct answer is B.

Multiple Choice Practice

SOLUTION

1–9x2

32x+6x2 10+=

2(x + 5)

(3x – 1) (3x + 1)

(3x + 1)Factor numerator and

denominator.

Problem A Recognize opposites

Simplify and state the excluded values.

x 2–167x–x 2 12+

Problem A Recognize opposites

Simplify and state the excluded values. x 2–167x–x 2 12+

x2–16

7x–x2 12+=

(4 – x) (4 + x)

(x – 3) (x – 4)Factor numerator and

denominator.

=– (x – 4) (4 + x)

(x – 3) (x – 4)=

– (x – 4) (4 + x)

(x – 3) (x – 4)

=– (4 + x)

x – 3

=x + 4

x – 3Write as .– a

b– b

a–

ANSWER The excluded values are –4 and 4.

Rewrite 4 – x as –(x – 4).

Divide out common factor.

Simplify.

Problem B

Simplify the rational expression. State the excluded values.

x 2 + 7x + 10

x 2 + 3x + 2

Problem B


x 2 + 7x + 10

x 2 + 3x + 2

x + 5x + 1

; –2, –5ANSWER

Guided Practice


y 2 – 16y + 64y 2 – 64

z 2 – 3z – 105 + 4z – z 2

Guided Practice


y 2 – 16y + 64y 2 – 64

z 2 – 3z – 105 + 4z – z 2

y – 8y + 8

; 8 –z + 2z + 1

; 5, –2

ANSWERANSWER


2) Excluded Value

3) Simplest Form

4) Factors

Vocabulary


2) Section 11.2 Pg. 692 3) Section ______

TxtBk. Problems #24-34 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?




Learning Target


MS Algebra Ch. 11.2 Simplifying Rational...

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