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Pre-Cal 20S December 17, 2008

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More work on rational equations.

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Pre-Cal 20S December 17, 2008

  1. 1. Still Working Those Equations Derivative Works by flickr user widdowquinn
  2. 2. You know how to multiply binomials right? (x + 1)(x - 3) then (x + 1)(x - 3) And how to factor trinomials? x 2- 2x -3
  3. 3. Fast Math to multiply numbers You know how to multiply -- 2 Digit Numbers binomials right? (x + 1)(x - 3) then (x + 1)(x - 3) And how to factor trinomials? x 2- 2x -3 What does this: http://www.youtube.com/watch?v=9qQAYEYLCoU have to do with that?
  4. 4. To solve rational equations, follow these steps: 1. Remove the denominators of the rational expressions by multiplying each rational expression in the equation by the least common denominator. For example, the least common denominator of the equation is
  5. 5. To solve rational equations, follow these steps: 2. Multiply each term by the least common denominator (e.g., 6x(x – 1)) to yield an equation with all denominators equal to 1. x=3 x=4
  6. 6. To solve rational equations, follow these steps: 3. Check your possible solution(s) for x. Check that neither of these numbers will cause any of the original denominators to equal 0. Since the restrictions are x≠1 and x≠0 it follows that x = 3 or x = 4 are the solutions to the original equation.
  7. 7. ` To solve rational equations, follow these steps: Note: Be careful not to confuse a rational expression and a rational equation. When simplifying a rational expression, the denominator remains (unless it cancels with a common factor in the numerator). In solving a rational equation, the denominator is cleared by multiplying both sides by the least common denominator.
  8. 8. Solve and state restrictions if any ... Solving Equations
  9. 9. Solve and state restrictions if any ... Solving Equations
  10. 10. Solve and state restrictions if any ... Solving Equations
  11. 11. Solve and state restrictions if any ... Solving Equations
  12. 12. Solve and state restrictions if any ... Solving Equations
  13. 13. Solve and state restrictions if any ... Solving Equations

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