Transcript Sect. 2.2 - Mt. San Jacinto College

Section 6.2 Adding & Subtracting
Rational Expressions
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Adding & Subtracting Rational Expressions
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Finding the LCD of 2 or more Polynomial Denominators
Adjusting Opposite Factors in Denominators
Adding & Subtracting Rational Expressions
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with the Same Denominators
with Unlike Denominators
1
-------------
+
1
-------------- =
6.2
?
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1
Adding and Subtracting Fractions with
Identical Denominators
Perform the operation:
6.2
2
Finding the LCD
(must be done before adding or subtracting 2 or more RE’s)
1. Factor each denominator
completely into primes.
2. List all factors of each
denominator.
(use powers when duplicate
factors exist)
3. The LCD is the product of each
factor to its highest power.
3
 4z 2
3
 4z 2
28z3 = (22) (7)(z3)
3
21z =
(3)(7) (z)
4z2
LCD= (22)(3)(7)(z3) Lacks↑
 (a  2)
 (a  2)
(a2 – 25) = (a + 5)(a – 5)
(a + 7a + 10) = (a + 5)
(a + 2)
LCD =6.2 (a + 5)(a – 5)(a + 2)
 (a  5)
 (a  5)
(a + 2)
(a – 5)
Lacks↑3
Find the LCD, using a Primes Table
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?
8(x – 3)
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?
(x2 – x – 6)
?
(2x2 – 12x + 18)
8(x – 3) = (2)3(x – 3)
(x + 2)(x – 3)
(x2 – x – 6) =
(x – 3)(x + 2)
8(x – 3)
(2x2 – 12x + 18) = (2) (x – 3)2
4(x + 2)
LCD = (2)3 (x – 3)2(x + 2)
Lacks↑
6.2
4
Adjusting an Opposite Denominator
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Situation: one factor is the opposite of the other
For
7
and 2
find the LCD
3(a – 2)
(2 – a)
For the second expression, multiply top and
bottom by -1 (doesn’t change its value)
Now
7 and -2
find the LCD
3(a – 2)
(a – 2)
Do this after factoring, before writing the LCD
6.2
5
Adding or subtracting rational expressions with
unlike denominators – note any exclusions
1. Find the LCD.
2. Express each rational
expression with a
denominator that is the
LCD.
3. Add (or subtract) the
resulting rational
expressions.
4. Simplify the result if
possible.
Exclusions: a ≠ ±2
6.2
6
Add & Subtract Practice - monomials
2
5
2 x
57
2 x  35
 2 
 2 
2
21x 3x
21x  x 3x  7
21x
21x  (3)(7) x
3 x  (3)
2
x
x
2
7
LCD  (3)(7) x
2
Lacks 
Exclusions: x ≠ 0
6.2
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Add & Subtract Practice - simplifying
x2
2x  2 y
x2
2( x  y )
 2



2
2
2
2
x  2 xy  y
x y
( x  y ) ( x  y )(x  y )
x2
2( x  y ) x 2  2 x  2 y


2
2
( x  y)
( x  y)
( x  y)2
x 2  2 xy  y 2  ( x  y ) 2
1
x  y  ( x  y)
( x  y)
LCD  ( x  y ) 2
Lacks 
6.2
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Add & Subtract Practice – change both
2 y 1
y 3
(2 y  1)( y  1)  ( y  3)( y  1)
 2


2
y  7 y  6 y  5y  6
( y  1)( y  6)( y  1)
2 y2  3y 1 y2  2 y  3
y2  y  4

( y  1)( y  6)( y  1)
( y  1)( y  6)( y  1)
y 2  7 y  6  ( y  1)( y  6)
( y  1)
y2  5y  6 
( y  1)
( y  6)( y  1)
LCD  ( y  1)( y  6)( y  1)
Exclusions: y ≠ ±1, 6
6.2
Lacks 
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Brain Break:
6.2
10
Add & Subtract – opposite monomials
3
1
3 1 2
1





8a  8a 8a 8a 8a 4a
LCD  8a
Exclusions: a ≠ 0
6.2
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Add & Subtract – opposite binomials
5x
3y  7
5 x + 1(3 y  7) 5 x  3 y  7




x  2y 2y  x x  2y
x  2y
x  2y
LCD  2 y  x
6.2
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Add & Subtract – function simplification
x 2  4  ( x  2)(x  2)
2x
5
1
x2
( x  2)
f ( x)  2


x 4 2 x 2 x
x  2  ( x  2)
2x
5
1
LCD  ( x  2)(x  2)
f ( x) 


( x  2)(x  2) x  2 x  2
2 x  5( x  2)  ( x  2) 2 x  5 x  10  x  2
f ( x) 

( x  2)(x  2)
( x  2)(x  2)
 4x  8
 4( x  2)
4



( x  2)(x  2) ( x  2)(x  2)
x2
6.2
Exclusions: x ≠ ±2
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What Next?
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6.3 Complex Fractions
next time
6.2
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