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Simplifying complex fractions

  1. Nov 2, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}[/tex]

    Should equal [tex]\left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I have tried numerous ways of trying to simplify the initial equation to equal the second, but cannot seem to get rid of the multi-term denominator.

    What is a good formula/method for reducing a fraction such as this?
  2. jcsd
  3. Nov 2, 2008 #2


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    Science Advisor

    When you have a denominator of the form [itex]1-\sqrt{A}[/itex], multiply numerator and denominator by [itex]1+\sqrt{A}[/itex].
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