I then add them together, and get:

(3^2x - 4 * 3^x + 3) / (2 * 3^x + 3) = 0

From here, I know that I can safely forget about the denominator, as it is only the numerator that is going to give me 0, so now I am at:

(3^2x - 4 * 3^x + 3) = 0

I put that through the quadratic formula, and find that 3^x is equal to 4, or 0. So I change this to a logarithm as such:

x log 3 = log 4

Divide both sides by log 3, and get log 4/log 3. Too bad the answer is 1 for this instance. (the other being 0, which at least works out) Can someone tell me where I have gone wrong? I have burnt 2 hours of my night trying to figure this out, and it is driving me absolutely crazy...

Thank you.