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Math Help - Rational Exponential Equation

  1. #1
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    Rational Exponential Equation

    Okay, I have a rational exponential equation on my final exam review sheet that I can't solve to save my life. I keep getting X=0 or X=2.something, but know that's not right because it's not one of the answers given. Here it is:

    x -x
    e + e
    _______ = 8
    x -x
    e - e
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  2. #2
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    Quote Originally Posted by cheeseokay View Post
    Okay, I have a rational exponential equation on my final exam review sheet that I can't solve to save my life. I keep getting X=0 or X=2.something, but know that's not right because it's not one of the answers given. Here it is:

    x -x
    e + e
    _______ = 8
    x -x
    e - e

    Multiply through by the denominator.

     e^x + e^{-x} = 8e^x - 8e^{-x}

    Now, if you multiply through by  e^x , you get the following:

     e^{2x} + 1 = 8e^{2x} - 8

    Now, if you remember that  e^{2x} = (e^x)^2 , then you can rearrange this equation to get a quadratic that is easily solved.
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  3. #3
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    Joined
    Nov 2009
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    Thanks! I finally got the problem right.
    Last edited by cheeseokay; December 6th 2009 at 11:44 AM.
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