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How to simplify this fraction?

  1. May 1, 2012 #1
    1. The problem statement, all variables and given/known data

    I want the simplify the following equation

    2. Relevant equations

    [itex]\frac{x}{{p}^{2}}+\frac{n-x}{{(1-p)}^{2}}[/itex], where p=[itex]\frac{x}{n}[/itex]


    3. The attempt at a solution

    I got this [itex]\frac{{n}^{2}}{x}-\frac{{n}^{2}}{n-x}[/itex], I don't think this is the right answer.
     
    Last edited: May 1, 2012
  2. jcsd
  3. May 1, 2012 #2

    HallsofIvy

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    No, that is not the right answer. How did you get that?
     
  4. May 1, 2012 #3
    [itex]=\frac{x{(1-p)}^{2}+{p}^{2}(n-x)}{{p}^{2}{(1-p)}^{2}} [/itex]
    [itex]=\frac{x}{{(\frac{x}{n})}^{2}}+\frac{n-x}{{(1-\frac{x}{n})}^{2}}[/itex]
    [itex]=x \frac{{n}^{2}}{{x}^{2}}+\frac{n-x}{({\frac{n-x}{n}})^{2}}[/itex]
    [itex]=\frac{{n}^{2}}{x}-(n-x)({\frac{n}{n-x}})^{2}[/itex]
    [itex]=\frac{{n}^{2}}{x}-\frac{{n}^{2}}{n-x}[/itex]

    Did I make a mistake somewhere?
     
    Last edited: May 1, 2012
  5. May 1, 2012 #4

    HallsofIvy

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    Why did you combine the fractions and then separate them again? In any case, the problem you posted had [itex]1- p^2[/itex], not [itex](1- p)^2[/itex] which you now have.

     
  6. May 1, 2012 #5
    I forgot to put parenthesis around 1-p in LaTex. It is fixed now.
     
  7. May 2, 2012 #6
    @HallsofIvy (PF Mentor) Are you still here? What do you think?
     
  8. May 2, 2012 #7

    SammyS

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    You changed a "+" sign above to a "−" sign below.
     
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