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.
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Ex. 1: Find
3
1

.
x2 x2
3
1
3 1


x2 x2 x2
4

x2
Since x + 2 is the common
denominator, add the numerators.
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3a  2 a  3

.
Ex. 2: Find
a7 a7
3a  2 a  3 (3a  2)  [(a  3)] Add the additive inverse of a - 3.


a7 a7
a7
3a  2  a  3

a7
Distributive Property
2a  5

a7
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

.
x2 2 x
x
x 1
x
x 1



x  2 2  x x  2  ( x  2)
x
x 1

 (
)
x2
x2
x
x 1


x2 x2
x  x 1

x2
2x 1

x2
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

rs
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
rs
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.