Post on 06-Apr-2018
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Simplifying
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Multiplying and Dividing
Rational Expressions
Remember that a rational number
can be expressed as a quotient of
two integers. A rational expression
can be expressed as a quotient oftwo polynomials.
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Remember, denominators
can not = 0.
Now,lets go through the steps to
simplify a rational expression.
Examples of rational expressions
2
4 8 4 7, ,
3 3 5 9
x y
x x y y
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Simplify:7x 7
x
2
1
Step 1: Factor the numerator and
the denominator completely lookingfor common factors.
Next
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7x 7 7(x1)
x2 1 (x1)(x1)
7x 7
x2 1
7(x1)
(x1)(x1)
What is the common factor?
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x1
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Step 2: Divide the numerator anddenominator by the common factor.
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7(x1)
(x 1)(x1)
7(x1)
(x 1)(x1)
1
1
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Answer: 7
x1
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Step 3: Multiply to get youranswer.
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Looking at the answer from the
previous example, what value ofx
would make the denominator 0?
x= -1
The expression is undefined when the
values make the denominator equal to 0
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How do I find the values
that make an expressionundefined?
Completely factor the originaldenominator.
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Ex:2ab(a 2)(b 3)
3ab(a2
4)
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Factor the denominator
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3ab(a2
4) 3ab(a 2)(a 2)
The expression is undefined when:
a= 0, 2, and -2 and b= 0.
ANSWER:
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Lets go through another example.
3a3 a4
2a3 6a2
3a3 a4
2a3
6a2
a3 (3 a)
2a2(a 3)
Factor
out the
GCF
Next
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3
2
2 ( 3)
(3 )a
a a
a
3 factored is 1( 3)a a
cancel like factors3
2
1 ( 3)
2 ( 3)
a a
a a
1
1
3
2
1( 3)
2 ( 3)
a
a a
a
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3
2
1
2
a
a
2cancel out the like factor a
1
2
a
1
a
answer
What values is the original expression undefined?
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Now try to do some on your own.
2
2
3 2
3 2
5 61)
9
5 102)
6 16
x x
x
x x
x x x
Also find the values that make
each expression undefined?
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Remember how to multiply fractions:
First you multiply the numerators
then multiply the denominators.
5 2:
6 20
Ex 10 1
120 12
5 2
6 20
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The same method can be used
to multiply rational expressions.
Ex:
4a2
5ab3
3bc
12a3 4 a a 3 b c
5 a b b b 12 a a a
11 1 1 1
1 1 1 1
c
5b2a2
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Lets do another one.
Ex:x3 3x2
x
2
5x
6
x2 10x 9
x
2
6x
27
Next
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Step #1: Factor the numerator
and the denominator.
x2
(x 3)(x 6)(x1)
(x1)(x 9)(x 9)(x3)
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Step #2: Divide the numerator and
denominator by the common factors.
x2 (x 3)
(x 6)(x1)
(x1)(x 9)
(x 9)(x3)
1
1
1
1
1
1
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Step #3: Multiply the numerator
and the denominator.x
2
x 6
Remember how to divide fractions?
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Multiply by the reciprocal of the
divisor. 45
1625
45
2516
4 25516
1
1
5
4
54
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Dividing rational expressions uses
the same procedure.
Ex: Simplify
y
2y
210y 24
y
2
2yy
2 2y 8
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y 2
y2
10y 24
y2 2y
y2
2y 8
y 2
y2
10y 24y2 2y 8
y2
2y
y 2(y 12)(y 2)
(y 4)(y 2)y(y 2)
1
1
1 1
Next
4( 12)y
y y
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Now you try to simplify the
expression:
x 3
x2 4x12
2x2 6x
x 2
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Answer:
1
2x(x 6)
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Now its you time!
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1)x + 3
2x3 2x2
x2 7x 6
x2 10x 21
2) 3x 67x 7
5x 1014x 14
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THESE ARE THE ANSWERS!!
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1)x 6
2x2
(x 7)
2) 6(x 1)
5( x 1)