Fractional Equations and Extraneous Solutions

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Fractional Equations and Extraneous Solutions

• Solving Rational Equations (not graphing) (7.10)

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POD

• Simplify this rational function.
• What is the shape of the graph?
• What is the restriction for x?

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Today we use rational expressions in equations
we solve for x.

• Lets start with this one.
• The Method
• Determine restrictions for x cant divide by 0.
• Find common denominator. Factoring can help.
• Adjust all terms with common denominator.
• Cancel the denominator in all terms.
• Solve the equation dont forget the
  restrictions! Those are the extraneous solutions.

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Follow the Method

1. Determine restrictions for x.

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Follow the Method

• x ? 2, -3
• 2. Find common denominator. Factoring can help.

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Follow the Method

• Adjust all terms with common denominator.

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Follow the Method

• Cancel the denominator in all terms.

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Follow the Method

• Solve the equation dont forget the
  restrictions! Those are the extraneous
  solutions.
• In this case, x 2 is extraneous.

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Try another

• Use the same method to solve this equation.
• What are the extraneous solutions?

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Try another

• Use the same method to solve this equation.
• How would you test these solutions?

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Try another

• Use the same method to solve this equation.
• What are the extraneous solutions?

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Try another

• Use the same method to solve this equation.
• Check the solutions.

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Try another

• Use the same method to solve this equation.
• What do you notice about the solutions?

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Try another

• Use the same method to solve this equation.
• This is true for every value of x. So, the
  solution set is all real numbers except 4 and -4.