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Math Help - pi^e and e^pi

  1. #1
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    pi^e and e^pi

    [pi^(e) + e^(pi)]/[e^(pi) - pi^(e)] =
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    Do you own a calculator or a computer algebra system?
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  3. #3
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    Quote Originally Posted by RTC1996 View Post
    [pi^(e) + e^(pi)]/[e^(pi) - pi^(e)] =
    Are you asked to evaluate this to a certain number of decimal places? Since this is transcendental, at the moment this is the exact answer.

    The best you can hope for to simplify it exactly is to turn it into a proper fraction.

    \displaystyle \frac{\pi^e + e^{\pi}}{e^{\pi} - \pi^e} = \frac{e^{\pi} - \pi^e + 2\pi^e}{e^{\pi} - \pi^e}

    \displaystyle = 1 + \frac{2\pi^e}{e^\pi - \pi^e}.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    Are you asked to evaluate this to a certain number of decimal places? Since this is transcendental, at the moment this is the exact answer.

    The best you can hope for to simplify it exactly is to turn it into a proper fraction.

    \displaystyle \frac{\pi^e + e^{\pi}}{e^{\pi} - \pi^e} = \frac{e^{\pi} - \pi^e + 2\pi^e}{e^{\pi} - \pi^e}

    \displaystyle = 1 + \frac{2\pi^e}{e^\pi - \pi^e}.

    You got it right. Thanks.
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