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anonymous

  • one year ago

Faction math!! please help!

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  1. anonymous
    • one year ago
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    Fraction or Factoring?

  2. anonymous
    • one year ago
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    x-2 / 3x-9 divided by x^2 + x - 6 / x^2-4x+3

  3. anonymous
    • one year ago
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    This is the question, Fraction division I suppose.

  4. anonymous
    • one year ago
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    are u looking for x

  5. anonymous
    • one year ago
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    It just says simplify your answer as much as possible

  6. mathstudent55
    • one year ago
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    I think you mean this, correct? \(\dfrac{x - 2}{3x - 9} \div \dfrac{x^2 + x - 6}{x^2-4x+3} \)

  7. anonymous
    • one year ago
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    yes mathstudent55 that's exactly how the problem looks

  8. mathstudent55
    • one year ago
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    You are dividing fractions. How do you divide a fraction by a fraction?

  9. anonymous
    • one year ago
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    Sort of but I'm taking a test and I havent seen the stuff in years (it's a final exam that I never took like 3 years ago and now I need it to graduate -.- so I have to take it and pass...)

  10. anonymous
    • one year ago
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    this is a question on the pretest packet

  11. mathstudent55
    • one year ago
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    For example: \(\dfrac{5}{8} \div \dfrac{3}{7} = \dfrac{5}{8} \times \dfrac{7}{3}\) you know the part above, right?

  12. anonymous
    • one year ago
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    yes.

  13. mathstudent55
    • one year ago
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    To divide a fraction by a fraction, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is just flipping the fraction.

  14. mathstudent55
    • one year ago
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    That means with our problem we can do that step, the flipping of the second fraction. \(=\dfrac{x - 2}{3x - 9} \times \dfrac{x^2-4x+3}{x^2 + x - 6} \) Ok so far?

  15. anonymous
    • one year ago
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    Okay I'm with you so far.

  16. mathstudent55
    • one year ago
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    Now we need to factor all numerators and denominators, and see what cancels out. \(=\dfrac{x - 2}{3(x - 3)} \times \dfrac{(x - 3)(x - 1)}{(x - 2)(x + 3)} \)

  17. anonymous
    • one year ago
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    Right that makes sense. So x-3 and x+3 would cancel out.

  18. mathstudent55
    • one year ago
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    No. Factors have to be exactly the same to cancel out.

  19. anonymous
    • one year ago
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    Oh..

  20. mathstudent55
    • one year ago
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    Notice the smae color means it can be canceled: \(=\dfrac{\color{red}{x - 2}}{3\color{green}{(x - 3)}} \times \dfrac{\color{green}{(x - 3)}(x - 1)}{(\color{red}{x - 2})(x + 3)}\)

  21. mathstudent55
    • one year ago
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    \(=\dfrac{\color{red}{\cancel{x - 2}}}{3\color{green}{(\cancel{x - 3})}} \times \dfrac{\color{green}{(\cancel{x - 3})}(x - 1)}{(\color{red}{\cancel{x - 2}})(x + 3)}\) What is left: \(=\dfrac{x - 1}{3(x + 3)} \)

  22. anonymous
    • one year ago
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    Okay.. so from there how can I simplify further?

  23. mathstudent55
    • one year ago
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    That is the final answer.

  24. mathstudent55
    • one year ago
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    You can leave it like that or like this: \(=\dfrac{x - 1}{3x + 9} \) Both forms are equally correct and acceptable.

  25. anonymous
    • one year ago
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    okay thank you very much!

  26. mathstudent55
    • one year ago
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    You're welcome.

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