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Math Help - Simplification

  1. #1
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    Simplification

    Can anybody show me how this

    \frac{-4x}{9\sqrt{4-\frac{4x^2}{9}}}

    winds up simplifying to this:

    \frac{-2x}{3\sqrt{9-x^2}}

    Here's what I have done, but I get a different answer:

    \frac{-4x}{9\sqrt{4-\frac{4x^2}{9}}}
    \frac{-4x}{9\sqrt{36-4x^2}}
    \frac{-4x}{9\sqrt{4(9-x^2)}}
    \frac{-4x}{9(2)\sqrt{9-x^2}}
    \frac{-2x}{9\sqrt{9-x^2}}

    I just don't see how that 3 winds up in the denominator. I get a 9.

    Thanks.
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  2. #2
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    Quote Originally Posted by joatmon View Post
    Can anybody show me how this

    \frac{-4x}{9\sqrt{4-\frac{4x^2}{9}}}

    winds up simplifying to this:

    \frac{-2x}{3\sqrt{9-x^2}}

    Here's what I have done, but I get a different answer:

    \frac{-4x}{9\sqrt{4-\frac{4x^2}{9}}}
    \frac{-4x}{9\sqrt{36-4x^2}} Wrong
    \frac{-4x}{9\sqrt{4(9-x^2)}}
    \frac{-4x}{9(2)\sqrt{9-x^2}}
    \frac{-2x}{9\sqrt{9-x^2}}

    I just don't see how that 3 winds up in the denominator. I get a 9.

    Thanks.
    \displaystyle \frac{-4x}{9\sqrt{4 - \frac{4x^2}{9}}} = \frac{-4x}{9\sqrt{\frac{36 - 4x^2}{9}}}

    \displaystyle = \frac{-4x}{\frac{9\sqrt{36-4x^2}}{3}}...

    Go from here...
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  3. #3
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    Got it. Thanks.
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