Post on 17-Apr-2018
transcript
1
Algebra
Chapter 12 Rational Expressions
2
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
3
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
12
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
=
=
=
14
Part 5: Divide Rational Expressions involving Polynomials.
Practice
=
=
=
15
Part 6: Divide Rational Expressions by a Polynomial.
Practice
a) fdfdf
=
=
16
Challenge Problem: Find the product in lowest terms.
Summary:
Exit Ticket:
17
Day 2: Homework
Multiply and reduce to simplest form.
1.
2.
3.
4.
5.
6.
7.
8.
18
Divide and reduce to simplest form.
9.
10.
11.
12.
13.
14.
15.
16.
19
Day 3 – Review of Simplifying, Multiplying and Dividing Rationals
20
21
22
23
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
24
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
26
Summary:
Exit Ticket:
27
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
28
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
29
Part 1: Identifying LCM
Find the LCM of the given expressions
A.
Practice:
***3.
30
(
)
(
)
(
)
(
)
31
Practice: Add or Subtract.
32
Challenge Problem: Add or subtract and simplify your answers.
Summary:
Exit Ticket:
33
Homework- (Day 5)
Add or subtract. Simplify your answer.
34
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)
35
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.
36
Example 3: Solve. Check your answer.
Practice: Solve. Check your answer.
5) 6)
xx
1
9
1
3
5
37
Challenge Problem: Solve. Check your answer.
Summary:
Exit Ticket:
9
x +
9
x - 2 = 12
38
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
39
Day 7 – Review of Adding/Subtracting and Solving Rational Equations
40
41
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)
42
40. 41.
42. 43.
44. 45.
46. 47.
40.
41.
42.
43.
44.
45.
46.
47.
40-47)
43
Day 8 – TEST REVIEW
Section 1: Excluded Values
Section 2: Simplifying Rational Expressions
44
Section 3: Multiplying and Dividing Rational Expressions
45
Section 4: Adding and Subtraction with Like Denominators
Section 5: Adding and Subtraction with Unlike Denominators
46
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.
47
More Practice!
48
49