Rational Expressions Part Two
This rational expression is already factored
             (written as multiplication),
Cancel identical factors on the top and bottom
X2+7x+12
X2+5x+6
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
X2+7x+12
(x+7)(x+1)
(x-6)(x-1)
(x-3)(x-4)
(x+3)(x+4)
Factors to:
X2+7x+12
X2+5x+6
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
(x+3)(x+4)
(x+6)(x+1)
(x+3)(x+2)
(x-6)(x-1)
(x-3)(x-2)
X2+5x+6
Factors to:
X2+7x+12
X2+5x+6
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
(x+3)(x+4)
(x+3)(x+2)
x+3
x+3
x+2
x+4
Click ALL the
boxes next to
the factors
that cancel
X2+7x+12
X2+5x+6
Simplified
Answer:
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
(x+2)
(x+4)
(x+3)(x+4)
(x+3)(x+2)
Click ALL the
boxes next to
the factors
that cancel
Recap: simplify
Factor
?
Cancel
?
X2+7x+12
X2+5x+6
Answer
?
X2+7x+10
X2+8x+15
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
X2+7x+10
(x+7)(x+10)
(x+1)(x+10)
(x+5)(x+2)
(x+5)(x+5)
Factors to:
X2+7x+10
X2+8x+15
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
(x+5)(x+2)
X2+8x+15
(x+3)(x+8)
(x+3)(x+5)
(x+1)(x+15)
(x+5)(x+10)
Factors to:
X2+7x+10
X2+8x+15
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
(x+5)(x+2)
(x+3)(x+5)
x+5
x+3
x+5
x+2
Click ALL the
boxes next to
the factors
that cancel
X2+7x+10
X2+8x+15
Rational expressions need to be
1. FACTORED  and then  2. CANCELED
Simplified
Answer:
(x+3)
(x+2)
(x+5)(x+2)
(x+3)(x+5)
Click ALL the
boxes next to
the factors
that cancel
Any top factor can be canceled with a bottom factor
?
Match each fraction part with the correct factor
(x+4)(x-4)
?
3x - 12
x2 - 16
(3)(x-4)
?
*
x2+x-12
(x+4)(x-3)
?
(x+3)(x-3)
?
x2 - 9
Check off all factor pairs that cancel
(x+4)(x-4)
(3)(x-4)
3
x+4
x-4
x-4
*
(x+3)(x-3)
(x+4)(x-3)
x+3
x+4
x-3
x-3
Simplified
Answer:
(x+4)(x-4)
(3)(x-4)
*
(x+3)
(x+3)(x-3)
(x+4)(x-3)
Can the 3's be simplified?
Yes
No, you can only simplfy (FACTORS),
Simplified
Answer:
(x+3)
3
Can the 3's be simplified?
No, you can only simplfy (FACTORS),
Simplified
Answer:
(x+3)
3
Which of these
can be simplified?
 7/7x
Every sum/difference
is one (FACTOR)
(7)(x)
(7)
 7/7+x
 7-x/x
(7+x)
(7-x)
(7)
(x)
Which of these
can be simplified?
Every sum/difference
is one (FACTOR)
(7)(x)
(7)
 7-x/x
(7+x)
(7-x)
(7)
(x)
Which of these
can be simplified?
 7/7x
Every sum/difference
is one (FACTOR)
x(x-4)
x
 7/7+x
 7-x/x
(x+3)(x-4)
(x-4)
x
x
Only this fraction has identical
(factors) on the top and bottom
x(x-4)
x
=
(x-4)
Only this fraction has identical
(factors) on the top and bottom
x(x-4)
x
=
(x-4)
1
(t)(h)(e)
(e)(n)(d)
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