ms algebra ch. 11.2 simplifying rational...
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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
Physical Representation
2. Draw a sketch
DAY 5
1. Review the word
Friendly definition
Physical Representation
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
Physical Representation
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
Find the excluded values, if any, of the expression.
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
Find the excluded values, if any, of the expression.
c.
9
4v
v 2 – +5
2+7w
w+8w 2
d.
Problem(s) B Find excluded values
Find the excluded values, if any, of the expression.
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
Find the excluded values, if any, of the expression.
6n –
125n2n 2 – – m 2
2m
– 4
Guided Practice
Find the excluded values, if any, of the expression.
6n –
125n2n 2 – – m 2
2m
– 4
, 42
3– 2–2,
ANSWERANSWER
Storm Check (Think, Write, Discuss, Report)
Why are excluded values important when simplifying rational expressions?
Excluded values are important when simplifying
rational expressions because _______________
_______________________________________
_______________________________________.
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 #4-10 Even Notes Copied on blank sheet #14-24 Even
Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
1) Rational Expression
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
Simplify the rational expression, if possible. State the excluded values.
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
Simplify the rational expression, if possible. State the excluded values.
22a 6
4a 3
c2c+ 5
Problem(s) B
Simplify the rational expression, if possible. State the excluded values.
22a 6
4a 3
c2c+ 5
11a 3
2; 0 c
2c+ 5
; – 5
ANSWERANSWER
Guided Practice
Simplify the rational expression, if possible. State the excluded values.
8s+2s 2
123s + 8x 3
8x
+ 16x 2
Guided Practice
Simplify the rational expression, if possible. State the excluded values.
8s+2s 2
123s + 8x 3
8x
+ 16x 2
; 432s – – 2;x 2
1+ 2x 0,
ANSWERANSWER
Storm Check (Think, Write, Discuss, Report)
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 __________________
_______________________________________
_______________________________________.
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 ________ Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
1) Rational Expression
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
Simplify the rational expression. State the excluded values.
x 2 + 7x + 10
x 2 + 3x + 2
x + 5x + 1
; –2, –5ANSWER
Guided Practice
Simplify the rational expression. State the excluded values.
y 2 – 16y + 64y 2 – 64
z 2 – 3z – 105 + 4z – z 2
Guided Practice
Simplify the rational expression. State the excluded values.
y 2 – 16y + 64y 2 – 64
z 2 – 3z – 105 + 4z – z 2
y – 8y + 8
; 8 –z + 2z + 1
; 5, –2
ANSWERANSWER
1) Rational Expression
2) Excluded Value
3) Simplest Form
4) Factors
Vocabulary
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
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?
Table of ContentsDate Description Date Due
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:
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