# Math Help - Rational Exponential Equation

1. ## 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

2. Originally Posted by cheeseokay
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.

3. Thanks! I finally got the problem right.