Algebra - White Plains Middle School...Section 2: Simplifying Rational Expressions 44 Section 3:...
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1 Algebra Chapter 12 Rational Expressions
Transcript of Algebra - White Plains Middle School...Section 2: Simplifying Rational Expressions 44 Section 3:...
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Algebra
Chapter 12 Rational Expressions
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Table of Contents
Day 1: Undefined &Simplifying Rational Expressions ………………….…………………………Page 3
HW: Pages 8 – 9 in Packet
Day 2: Multiplying and Dividing Rational Expressions ……………………………..……………… Page 10
HW: Pages 17 – 18 in Packet
Day 3: Review of Dividing Rational Expressions ……………………………….…..…………… Page 19
HW: Pages 19 – 22 in Packet
Day 4: QUIZ
Day 4: Adding & Subtracting Rational Expressions (Same Denominators) …………………….……Page 23
HW: Page 27 in Packet
Day 5: Adding & Subtracting Rational Expressions (Unlike Denominators) …………………….… Page 28
HW: Page 33 in Packet
Day 6: Solving Rational Expressions using the LCD ……………………………………….…………Page 34
HW: Page 38 in Packet
Day 7: Review of Adding /Subtracting and Solving Rational Expressions using the LCD .…………Page 39
HW: Pages 39 – 42 in Packet
Day 8: QUIZ
Day 9 – Review
Pages 43 – 49 in Packet
Day 10 - Test
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Chapter 12 – 3 (Day 1) SWBAT: Simplify rational expressions and identify excluded values of rational expressions.
Warm – Up
Reduce to lowest terms.
Example 1: Find the value for x that makes the fraction undefined (excluded values):
Practice: Find the value for x that makes the fraction undefined (excluded values):
c. 2x+1
x2- 15xa.
6
x+4b.
3
3x-6
a. 14x2
2x b. 3x5
6x3 c. 15x2
35x4a.
30x3y5
6x2y3
4
a) 2x-10
2x b) 4x-8
4x c) 5x-15
5x
1) 10x-20
102)
3x-9
3x 3) 4x-12x
4x
a) 3x-15
x-5
b) 6x-12
x-2
3) 4x-6
2x-3
Example 2: Reduce to lowest terms (factoring and cancelling).
Practice: Reduce to lowest terms.
**
Think:
= =
= = =
5
a) x+5
x2+4x-5b)
x-1
x2-2x+1
Example # 3: Reduce to lowest terms (factoring trinomials and cancelling).
Practice: Reduce to lowest terms.
Example 4: Reduce to lowest terms (factoring numerator and denominator)
Practice: Reduce to lowest terms
**
2) x+1
x2+5x+41)
x+3
x2-x-12
a) x2-4
x2-8x+12
b) x2-25
x2+10x+25c)
2x-4
x2+4x-12
1) x2-4
x2+4x+42)
x2-25
x2+2x-153)
5x+5
x2-4x-5
Think:
= =
= =
Think:
6
Example 6: Recognize Opposites. Simplify if possible and state the excluded values
Case 1:
Case 2:
Case 3:
Note:
__________________________________________________________________________________________
__________________________________________________________________________________________
Example:
Practice:
=
=
7
2) 4x-x2
x2-16
Challenge Problem:
Simplify.
Summary:
Exit Ticket:
8
Homework (Day1)
Reduce to lowest terms (factoring and cancelling).
9
Reduce to lowest terms (factoring and cancelling).
16) 17)
18) 19)
10
Chapter 12 – 4 (Day 2)
SWBAT: Multiply and Divide rational expressions
Warm – Up
1. Gfg 2.
= =
= = =
11
1) 24x
35y14y
8x
Practice: Find the product in lowest terms.
6) 24x3y2
7z321z2
12xy
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Practice: Find the product in lowest terms.
Part 3: Multiply Rational Expressions Involving Trinomial Polynomials.
=
13
Practice
Part 4: Multiply a Rational Expression by a Polynomial.
Practice
=
=
=
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Part 5: Divide Rational Expressions involving Polynomials.
Practice
=
=
=
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Part 6: Divide Rational Expressions by a Polynomial.
Practice
a) fdfdf
=
=
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Challenge Problem: Find the product in lowest terms.
Summary:
Exit Ticket:
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Day 2: Homework
Multiply and reduce to simplest form.
1.
2.
3.
4.
5.
6.
7.
8.
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Divide and reduce to simplest form.
9.
10.
11.
12.
13.
14.
15.
16.
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Day 3 – Review of Simplifying, Multiplying and Dividing Rationals
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21
22
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ADDING AND SUBTRACTING RATIONALS (Day 4)
SWBAT: To add and subtract rational expressions with the same denominators.
QUIZ
Example 1: Add the fractions and reduce to lowest terms.
c) 2m + 4
m2 - 9 +
2
m2 - 9
a) 7
12 -
1
12b)
7x
12 -
x
12c)
7
12x -
1
12x
2. Subtract and simplify your answer.
c) 5
6 +
1
6a)
4
9 +
2
9b)
4x
9 +
2x
9
1. Add and simplify your answer.
Warm _Up
a) 3b
b2 +
5b
b2
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Practice: Add the fractions and reduce to lowest terms.
1) 2)
3) 4)
Example 2: Subtract the fractions and reduce to lowest terms.
3
6
3
2
xx
x
5a + 2
a2 - 4 -
2a - 4
a2 - 4
b) 3m - 6
m2 + m - 6 -
-m + 2
m2 + m - 6
c)
8
4
8
2 xx
9
3
9 22 xx
x
d
c
d
c
12
9
12
19
10x
5y -
2x
5y
a)
25
Practice: Subtract the fractions and reduce to lowest terms.
7) 8)
9) 10)
Challenge Practice:
13)
y
b
y
b
3
4
3
11
62
64
62
48
x
x
x
x
1
65
1
5622 x
x
x
x
yx
yxy
yx
xyx
2
2
2
2 22
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Summary:
Exit Ticket:
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Homework - (Day 4)
Add or Subtract. Simply your answer.
1) 2)
3) 4)
5) 6)
7) 8)
9) 10)
22 3
5
3 x
x
x
x
16
4
16 22 xx
x
33
44
y
y
y
y
3
3
3
122
xx
x
33 2
3
2
7
xx
6
6
6
2
x
x
x
x
22
22
22
3 22
x
xx
x
xx
254
8
254
322 x
c
x
x
65
1
65
13422 xxxx
x
23
65
23
2722 xx
x
xx
x
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Adding and Subtracting Rationals (Day 5)
SWBAT: To add and subtract fractions with unlike denominators.
Warm Up
Add and simplify your answer.
9
72
9
8322 x
x
x
x
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Part 1: Identifying LCM
Find the LCM of the given expressions
A.
Practice:
***3.
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(
)
(
)
(
)
(
)
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Practice: Add or Subtract.
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Challenge Problem: Add or subtract and simplify your answers.
Summary:
Exit Ticket:
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Homework- (Day 5)
Add or subtract. Simplify your answer.
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Chapter 12 – 7 Solving Rational Equations (Day 6)
SWBAT: Solve Rational Expressions by Using the LCD.
Warm Up
1. Gfdg 2.
Solving a Rational Equation Example 1: Solve.
Practice
1) 2)
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Example 2: Solving a Rational Equation
Practice: Solve. Check your answer.
3) 4)
2
7
5
3
10
xx
2
1
3
1
6
x2
2
1
8
5
x
Step 1: Find the LCD
Step 2: Multiply every term by the LCD
Step 3: Simplify and solve.
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Example 3: Solve. Check your answer.
Practice: Solve. Check your answer.
5) 6)
xx
1
9
1
3
5
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Challenge Problem: Solve. Check your answer.
Summary:
Exit Ticket:
9
x +
9
x - 2 = 12
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Homework (Day 6)
Solve. Check your answer.
1) 2)
3) 4)
5) 6)
7) 8)
6
15
4
1
3
8
xxx
6
5
3
21
xx
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Day 7 – Review of Adding/Subtracting and Solving Rational Equations
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25-30) Simplify each rational expression by adding/subtracting. Box your answers and factor/simplify at the end, if need be.
25.
26. 27.
28.
29. 30.
31-39)
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40. 41.
42. 43.
44. 45.
46. 47.
40.
41.
42.
43.
44.
45.
46.
47.
40-47)
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Day 8 – TEST REVIEW
Section 1: Excluded Values
Section 2: Simplifying Rational Expressions
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Section 3: Multiplying and Dividing Rational Expressions
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Section 4: Adding and Subtraction with Like Denominators
Section 5: Adding and Subtraction with Unlike Denominators
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Section 6: Solving Rational Equations
Solve each equation. Check your answer
Step 2: Multiply everything by the LCD
F.O.I.L. on the left and Distribute on the right
Set Quadratic Equation equal to zero.
Factor out GCF
Set up a “T” chart and solve for x.
Step 1: Find the LCD
Step 3: Simplify and Solve.
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More Practice!
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