Rational Functions

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Rational Functions

• Rational Functions and Variations
• Simplifying Rational Expression

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Rational Function (7.1)

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Inverse Variation(7.1)

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Modeling(7.1)

• A group of students in the chess club want to
  rent a bus to take them to a national chess
  competition. The bus cost 1500 to rent and can
  hold up to 60 people.
• Write an equation that models the given
  information.
• Cost per student if 30 students take the bus.
• What is a reasonable domain and range?

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Inverse Variation(7.1)

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Direct Variation(7.1)

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Car Repair(7.1)

• The cost for labor at an auto repair shop is
  directly proportional to the time the mechanic
  spends working on the car. If the mechanic works
  on the car for five hours the labor cost is 325.
• Write an equation that models the labor cost at
  the auto shop.
• What is the labor cost for two hours of work?

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Domain(7.1)

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Example (7.1)

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1 Rule (7.2)

• Simplify
• all
• fractions

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Methods (7.2)

1. Factor
2. Long Division
3. Synthetic Division

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Factor (7.2)

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Special case factoring

• 7(x 5)
• (5 x)
• Rewrite the denominator with the variable
  expression first
• 7(x 5) 7(x 5) 7(x 5)
• (5 x) (-x 5) -1(x 5)
• -7

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Long Division

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Synthetic Division

• Condenses the steps of long division without all
  the detail.
• Performing Synthetic Division
• The divisor (polynomial in the denominator) must
  be a binomial of the form x c
• Use only the coefficients of each term and not
  the variables

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Example

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Practice

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Multiplying/Dividing(7.3)

• The rules for fractions still apply when working
  with rational expressions!
• Multiplication
• 2ox 6xy
• 18y2 10

1. Factor the numerator and the denominator
2. Divide out common factor
3. Rewrite as a single fraction in factored form

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Dividing

• x 3 x 4
• x 7 x 7

Keep Change Flip Factor the numerator and
denominator (if possible) Divide out common
factors and leave in factored form
x 3 x 7 x 3 x 7 x 4
x 4
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Adding/Subtracting

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Practice

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Practice

• h 14 h 6
• (h 5) (h 4) h 4
• a 2 a 3
• a2 5a 6 a2 8a 12

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Subtraction

• Be careful!
• The numerator of the second fraction changes sign
  in subtraction.
• x2 5x - 3x 8
• (x 3)(x 4) (x 3)(x 4)

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Complex Fraction

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