Six Sigma 8.5 Rational Expressions with Like Denominators CORD Math Mrs. Spitz Fall 2006 Six Sigma Objective • Add and subtract rational expressions with like denominators.
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Transcript Six Sigma 8.5 Rational Expressions with Like Denominators CORD Math Mrs. Spitz Fall 2006 Six Sigma Objective • Add and subtract rational expressions with like denominators.
Six Sigma
8.5 Rational Expressions with
Like Denominators
CORD Math
Mrs. Spitz
Fall 2006
Six Sigma
Objective
• Add and subtract rational expressions
with like denominators.
Six Sigma
Upcoming
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8.5 Tuesday/Wednesday – Skip 8.6
8.7 Thursday 10/26
8.8 Friday 10/27
8.9 Monday 10/30
8.10 Tuesday/Wed
Chapter 8 Review Wed/Thur
Chapter 8 Test Friday
Six Sigma
Assignment
• Pg. 324 #4-41 all
• Midchapter Review pg. 325 #1-11
Six Sigma
Introduction
• To add or subtract fractions with like
denominators, you add or subtract the
numerators. Then you write the sum or
difference over the common
denominator.
3 2 5
7 7 7
7 2 5
9 9 9
You can use these same methods to add or subtract
rational expressions.
Six Sigma
Ex. 1: Find
3
1
.
x2 x2
3
1
3 1
x2 x2 x2
4
x2
Since x + 2 is the common
denominator, add the numerators.
Six Sigma
3a 2 a 3
.
Ex. 2: Find
a7 a7
3a 2 a 3 (3a 2) [(a 3)] Add the additive inverse of a - 3.
a7 a7
a7
3a 2 a 3
a7
Distributive Property
2a 5
a7
Remember when subtracting rational expressions to
add the additive inverse of the second expression.
Six Sigma
Express in simplest form.
• When adding or subtracting fraction,
sometimes the result can be expressed
in simplest form.
3 1 4 1
8 8 8 2
The GCF of 4 and 8 is 4.
9 3
6 3
16 16 16 8
The GCF of 6 and 16 is 2.
Six Sigma
8n 3 2n 5
.
Ex. 3: Find
3n 4 3n 4
8n 3 2n 5 (8n 3) (2n 5)
3n 4 3n 4
3n 4
8n 3 2n 5
3n 4
2(3n 4)
(3n 4)
2
Since 3n+4 is the common
denominator, subtract the
numerators.
Combine like terms.
Factor out a 2 out of the
numerator and cancel 3n+4 from
both numerator and denominator.
Six Sigma
Ex. 4: Find
x
x 1
.
x2 2 x
x
x 1
x
x 1
x 2 2 x x 2 ( x 2)
x
x 1
(
)
x2
x2
x
x 1
x2 x2
x x 1
x2
2x 1
x2
Rewrite 2 – x as x – 2 by
multiplying by -1.
Remember
1
1
x
x
Simplify and combine like terms.
Six Sigma
Example 5: Application
• Find the measure of
the perimeter of the
rectangle.
r
r 2 s2
s
2
2
r s
Ex. 5: Find the measure of the
perimeter of the rectangle. r s s
2
Six Sigma
P 2l 2w
2(
2r
2s
2 2 2 2
r s
r s
2(r s)
(r s)( r s )
2
rs
2
← Perimeter formula for rectangle.
r
s
)
2
(
)
2
2
2
2 ←
r s
r s
2r 2 s
2 2
r s
r
r 2 s2
Substitute values.
← Distributive Property
← Combine like terms
← Factor out 2 as common factor and
cancel terms that are same in
numerator and denominator.
The measure of the perimeter is:
2
rs
Six Sigma
Upcoming
• Midchapter Quiz – 20 points apiece so I can see how
you are doing.
• Skipping 8.6
• 8.7 Rational expression with Unlike Denominators.
• 8.8 Mixed expressions and complex fractions.
• 8.9 Solving Rational Equations
• 8.10 Application: Formulas.
• Chapter 8 Review
• Chapter 8 Exam
• Binder Check. Make sure you have all notes from
each section, or download off the web. You must
recopy to get full credit.