Rational Expressions Finding LCD Algebra
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Rational Expressions Finding LCD
Algebra
1
5
2
5
Review: Adding FractionsYou can only add like to like
Same Denominators
1
5
2
5
3
5
Different DenominatorsMake them the same
find a common denominator
The product of all denominators is always a common denominatorBut not always the least common denominator
Finding the LCD
Example:
1
12
4
15
Factor the Denominators
15 3 5 12 2 2 3
Assemble LCD
15 3 5 12 2 2 3
2 2 3 5 60
Each factor in the denominators needs to be used at least once in the LCD.
Build up Fractions to LCD
1
12
4
15
×5
×5
×4
×41
12
4
15
5
60
16
60
Add Numerators
5
60
16
60
5
60
16
60
21
60
5
60
16
60
21
60
7
20
And Reduce if Needed
12
2
6
2 nn
12
2
26
22 nn
12
2
12
4 nn
12
6n
2
n
Rational Expressions
Example:
x
x
x
x x
1
1
2
2 12 2
Factor the Denominators
x x x2 1 1 1 ( )( )
x xx x
2 2 11 1
( )( )
Assemble LCD
( )( )x x 1 1
( )( )x x 1 1
( )( )( )x x x 1 1 1
DE
NO
MIN
AT
OR
S
Each factor in the denominators needs to be used at least once in the LCD.
Build up Fractions to LCD
x
x x
x
x x
1
1 1
2
1 1( )( ) ( )( )
LCD x x x ( )( )( )1 1 1
x ( )1
x ( )1)( x( )1
x( )1FACTORED
DENOMINATORS
Add Numerators
( )( ) ( )
( )( )( )
x x x x
x x x
1 1 2 1
1 1 1
x x x x
x x x
2 22 1 2 2
1 1 1
( )( )( )
Simplify Numerator
3 1
1 1 1
2x
x x x
( )( )( )
( )( ) ( )
( )( )( )
x x x x
x x x
1 1 2 1
1 1 1
Summary of Steps
1. Factor denominators
2. Assemble LCD
3. Build up Fractions
4. Add/Subtract Numerators
5. Simplify Numerator
6. Reduce Factors if Possible
Add or subtract as indicated.
2
3
9 2 6
x
x x
3
( 3)( 3) 2( 3)
x
x x x
So the LCD is 2(x + 3)(x – 3)
3
2( 3)( 3) 2( 3)( 3)
x
x x x x
(2) ( 3)x 2 3( 3)
2( 3)( 3)
x x
x x
2 3 9
2( 3)( 3)
x x
x x
5 9
2( 3)( 3)
x
x x
Subtract So the LCD is (x – 2)(x + 3)(x – 3)
2 2
6
9 5 6
x x
x x x
6
( 3)( 3) ( 2)( 3)
x x
x x x x
6
( 2)( 3)( 3) ( 2)( 3)( 3)
x x
x x x x x x
( 2)x ( 3)x
6 ( 2) ( 3)
( 2)( 3)( 3)
x x x x
x x x
2 26 12 3
( 2)( 3)( 3)
x x x x
x x x
25 15
( 2)( 3)( 3)
x x
x x x
5 ( 3)
( 2)( 3)( 3)
x x
x x x
5
( 2)( 3)
x
x x
Rational Expressions Finding LCD
Algebra 1 &
Algebra 1 Honors
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