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Partial Fractions turn out wrong

  1. Sep 21, 2009 #1
    Here's (what I think is) a step in partial fractions that I don't understand:
    http://apthtml.com/images/partialfrac.png [Broken]

    I'm taking the regular partial fractions steps and I keep ending up with 1 / (1 - x) rather than 1 / (x - 1). What am I doing wrong?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 21, 2009 #2
    Are the signs the same as well? Remember, -1/(x-1) = 1/(1-x).
     
    Last edited by a moderator: May 4, 2017
  4. Sep 21, 2009 #3

    sylas

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    Science Advisor

    You don't show your steps, so I don't know what you are doing wrong. But try this. Let x be 0.5.

    [tex]\begin{align*}
    x &= 0.5 \\
    \frac{1}{x(1-x)} &= \frac{1}{0.5 \times (1 - 0.5)} \\
    & = \frac{1}{0.5 \times 0.5} \\
    &= \frac{1}{0.25} \\
    & = 4 \\
    \frac{1}{x} - \frac{1}{x - 1} &= \frac{1}{0.5} - \frac{1}{0.5 - 1} \\
    & = 2 - -2 \\
    & = 4 \\
    \frac{1}{x} - \frac{1}{1 - x} &= \frac{1}{0.5} - \frac{1}{1 - 0.5} \\
    & = 2 - 2 \\
    & =0
    \end{align*}[/tex]​

    So you can see the second form has to be wrong.

    If you can't see which step of your argument is false, just substitute 0.5 for x at all points, and see at which step you get the wrong answer. Stare at that step until you are enlightened.

    Cheers -- sylas
     
    Last edited by a moderator: May 4, 2017
  5. Sep 21, 2009 #4
    slider: that's definitely the case here, subtle switching of signs and a reversal rule I wasn't aware of. I suppose knowing these rules just comes with doing a lot of math.

    silas: I appreciate the detailed answer, and particularly your advice to "Stare at that step until you are enlightened." I feel like I do that quite often... and it works!
     
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