Download SPI 3102.2.1 Operate (add, subtract, multiply, divide, simplify

Name:
Date:
Period:
Radical and Rational Functions
Simplify Radical/Rational Expressions-Add/Subtract/Multiply/Divide Radical Expressions
Multiply/Divide Rational Expressions
Lesson: 11-6/11-7/11-8/12-3/12-4
Packet 10
Tennessee State Standard
Common Core State Standards
SPI 3102.2.1 Operate (add, subtract,
multiply, divide, simplify, powers) with
radicals and radical expressions
including radicands involving rational
numbers and algebraic expressions.
ACED-1 Create equations and
inequalities in one variable and use
them to solve problems. Include
equations arising from linear and quadratic
functions, and simple rational and
exponential functions.
SPI 3102.1.3 Apply properties to
evaluate expressions, simplify
expressions, and justify solutions to
problems.
SPI 3102.3.4 Operate with, evaluate,
and simplify rational expressions
including determining restrictions on the
domain of the variables.
1
Name:
Date:
The student will simplify radical
expressions.
Period:
Radical Expression
11-6
An expression that contains a radical sign (√ ) is a __________________.
The expression under a radical sign is the ________________.
Product Property
Quotient Property
=
=
=
=
2
Name:
Date:
Part A
3
Period:
Name:
Date:
Part B
4
Period:
Name:
The student will add and
subtract radical expressions
Date:
Adding and Subtracting Radical
Expressions
Steps
1) Simplify each radical
2) Combine like radicals ( must
have the same radicand)
5
Period:
11-7
Name:
Date:
6
Period:
Name:
The student will multiply and
divide radical expressions and
rationalize denominators.
Date:
Period:
Multiplying and Dividing Radical
Expressions
11-8
Multiplying Square Roots
1) Multiply the radicands
2) Multiply the coefficients
3) Simplify the radicands using
Expansion tree
Multiplying Using Distributive Property
1) Distribute
2) Use product property
Of square roots
(5 +
Multiplying Sums and Differences of Radicals
1) Use the rectangle method
2) Simplify by combining like terms
(4 +
Rationalizing the Denominator
1) Multiply the top & bottom by the
Denominator
2) Use product property of square roots
3) Simplify if needed
7
)
(
Name:
Date:
Period:
Part A
12
5
3 10y
3
8
2 7
6y
6
8
3
12
2 5
2
13
6
50t
8
2
2 5b
2
2
2x
7
10b
5
3 7
8x
5
2x
3
Name:
Date:
Period:
Part B
2
2
3 6
7
5
10
5m
4
3 6 3 6
4
3 2
5
2
3
6
5
2 6
7
15
2
5
2
3
3a
2
75k
32
17
10 2k
48z
9
8
Name:
The student will simplify
rational expressions and
identify excluded values of
rational expressions.
Date:
Simplifying Rational Expressions
Identifying Excluded Values
1) Set the denominator equal
To 0.
2) Factor if necessary
3) Solve for the variable
Simplify rational expressions
1) Factor numerator &
denominator If factorable.
2) Find the excluded
Values.
3) Look for common
factors in Numerator
and denominator.
4) Divide out common
FACTORS!
Simplify Rational Expressions
Using Opposite Binomials
1) Follow the steps above
2) Identify opposite binomials
Ex: (x-7) and (7-x)
3) Divide out opposite binomials
To get a factor of -1.
10
Period:
12-3
Name:
Date:
Period:
Part A
Simplify and find the excluded values for each rational expression.
5x 2
10 x
5x
3x 6
2
x
3x 2
x2
x2
4x
4x
5 5x
x2 1
5
3
2x
4x
2
x
x
2
x2
x
2
x
2
3
6x
6
7x 6
2x
2x 8
x
6x 9
11
x
x 3
2x 15
2
x2
x
2
x2
49
8x 7
x 12
4 x
6
3
x
Name:
Date:
Period:
Part B
Simplify and find the excluded values for each rational expression.
4x
x
4x
x
2
4x 2
2x
x2
2x
x
2
2
x
8 x
6x 16
*
x 1
x2 4
5
25
5
4x 7
20 x
10
1
3x 5
2
x 2 4x 5
x 2 8 x 15
x2
10 x 2 360
5 x 2 30 x
10
3 x
2x 6
x2
x2
12
25
3x x 2
4x
4x
5
3
Name:
The student will simplify
rational expressions and
identify excluded values of
rational expressions.
Multiplying Rational Expressions
Date:
Period:
Multiplying and Dividing
Rational Expressions
6a 12
3a a2
a 3
4a2 8a
12-4
9rt 5
5r 4
10r 2
27t
1) Factor numerator &
denominator If factorable.
2) Look for common
factors in Numerator
and denominator.
4) Divide out common
FACTORS! (Top to Bottom)
5) Multiply numerators then
Denominators.
Dividing Rational Expressions
x4y
3z 5
x 2 z3
9y 2 z
1) Rewrite as a multiplication
Problem. (same-change-flip)
2) Factor numerator &
denominator If factorable.
3) Look for common
factors in Numerator
and denominator.
4) Divide out common
FACTORS! (Top to Bottom)
5) Multiply numerators then
Denominators.
13
8n2 8
10n 10n2
(2n3
6n2
8n)
Name:
Date:
Period:
Part A
8a2b5
a3
c 4d
9c
3x 2
2y 4
4x 8
3
3a2
4b9
2cd 8
3c 4d 2
4 xy 4
x6
7
2t
k2
6
6x
x 2
t2
t
12
8k 2 24k
2k 2
6k 9
k 1
14
3c 2 24c
c 2 2c 1
5 j 2k 2
3 jk 5
3x 2
xy 3
y
3
c2
9c 8
9c 9
10 j 2k
9 j3
2xy 8y
4x x 2
Name:
Date:
Period:
Part B
q5
pq 4 p
2q 8
6q 2
x
1
5
6x 6
7
3
x
2
÷
5
x
2
.
2m
5m 20
ab
5ab 5b
(m 2
a2
2x 4
÷(x
x2
15
16)
3a
2)
p 3
p2 25
3 p 15
p2 p 6
8x 2 y 3
2xy
4
m2
2
4m
2
8m
xy
3
8m 12
6 m