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Fractional Equations and Extraneous Solutions

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Fractional Equations and Extraneous Solutions Solving Rational Equations (not graphing) (7.10) POD Simplify this rational function. What is the shape of the graph? – PowerPoint PPT presentation

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Title: Fractional Equations and Extraneous Solutions


1
Fractional Equations and Extraneous Solutions
  • Solving Rational Equations (not graphing) (7.10)

2
POD
  • Simplify this rational function.
  • What is the shape of the graph?
  • What is the restriction for x?

3
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.

4
Follow the Method
  1. Determine restrictions for x.

5
Follow the Method
  • x ? 2, -3
  • 2. Find common denominator. Factoring can help.

6
Follow the Method
  • Adjust all terms with common denominator.

7
Follow the Method
  • Cancel the denominator in all terms.

8
Follow the Method
  • Solve the equation dont forget the
    restrictions! Those are the extraneous
    solutions.
  • In this case, x 2 is extraneous.

9
Try another
  • Use the same method to solve this equation.
  • What are the extraneous solutions?

10
Try another
  • Use the same method to solve this equation.
  • How would you test these solutions?

11
Try another
  • Use the same method to solve this equation.
  • What are the extraneous solutions?

12
Try another
  • Use the same method to solve this equation.
  • Check the solutions.

13
Try another
  • Use the same method to solve this equation.
  • What do you notice about the solutions?

14
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.
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