Multiplying and Dividing Rational Expressions

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Section 9.4

• Multiplying and Dividing Rational Expressions

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Multiplying and Dividing Rational Expressions

• A rational expression is considered to be
  simplified when its numerator and denominator
  have no common factors left

Factor the numerator and denominator...
Example Simplify
Cancel common factors...
2x
Reduce...
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Multiplying Fractions
(Parenthesize polynomials for clarity) To
Simplify Factor, then cancel like factors
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Example Step by Step
x
1
1
4
1
1

1. Write down original problem
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Practice - Rational Multiplication

1. Write down original problem
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Practice - Rational Multiplication

1. Write down original problem
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Practice - Rational Multiplication

1. Write down original problem
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Multiplying rational expressions works the same
as multiplying fractionsyou may multiply
numerators and denominators and then simplify, or
you can cross cancel common factors...
Example Multiply
With monomials, its a good idea to multiply
first, and then simplify...
Now reduce...
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3
4y3 3
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With polynomials, factor each numerator and
denominator, if factorable, and cross cancel to
simplify...
Example Multiply
Factor...
Cross cancel...
x 1 x
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Recall that to divide fractions, you can invert
and multiply ...
Example Divide
Rewrite as multiplication...
Factor...
Cross cancel...
6x2 3x
2x
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Finding Powers of Rational Expressions

• Factor and Simplify (if possible) before applying
  the power
• If part of a larger expression, see if any terms
  cancel out
• Usually leave in factored form (unlike the text
  example)

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Dividing Fractions
Change to multiplication by reciprocal, then
follow the procedure for multiplication
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Practice - Rational Division

1. Write down original problem1a. Rewrite as
   multiplication by reciprocal
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Practice - Rational Division

1. Write down original problem1a. Rewrite as
   multiplication by reciprocal
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Practice - Rational Division

1. Write down original problem1a. Rewrite as
   multiplication by reciprocal
2. Combine with parenthesized polynomials
3. Factor polynomials (if possible)
4. Rewrite (if any factoring was done)
5. Cancel out matching factors
6. Simplify the answer

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Mixed Operations

• Multiplications Division are done left to right
• In effect, make each divisor into a reciprocal

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Assignment

• Section 9.4 page 558 559
• 18 48 (every 3rd)