1. ## pi^e and e^pi

[pi^(e) + e^(pi)]/[e^(pi) - pi^(e)] =

2. Do you own a calculator or a computer algebra system?

3. Originally Posted by RTC1996
[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.

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

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

4. Originally Posted by Prove It
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.

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

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

You got it right. Thanks.