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Math Help - Rationalizing the denominator of a radical fraction

  1. #1
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    Rationalizing the denominator of a radical fraction

    This is for my trigonometry class but it's only a small portion of a bigger problem so I'm posting it here. Here is a picture of my issue:

    http://i.imgur.com/cfxLe.png

    How can I get that final answer? I know to rationalize a denominator I have to multiply both sides by the bottom radical, but that one seems more complicated. Help is appreciated.
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  2. #2
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    Re: Rationalizing the denominator of a radical fraction



    ...

    \frac{15-7\sqrt{15}}{15+7\sqrt{15}} \cdot \frac{15-7\sqrt{15}}{15-7\sqrt{15}} =

    \frac{15^2 - 14 \cdot 15 \sqrt{15} + 49 \cdot 15}{15^2 - 49 \cdot 15} =

    \frac{15(15 - 14 \sqrt{15} + 49)}{15(15 - 49)} =

    \frac{64 - 14 \sqrt{15}}{-34} =

    \frac{7\sqrt{15}-32}{17}
    Thanks from bobsanchez
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  3. #3
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    Re: Rationalizing the denominator of a radical fraction

    General:
    (a - b) / (a + b) = (a^2 - 2ab + b^2) / (a^2 - b^2)

    Your a is 15, your b is 7SQRT(15); throw 'em in there !
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