That is just
I know that the answer to this limit is -.5, but I can't prove it algebraically. I know that I have to mutiply by "1" somehow, but I've tried many conjugates, etc, and I just can't get anywhere. (It's hard to read, but it's supposed to be the limit as x approaches negative infinity...)
lim x→-∞ ((-2)^x+3^x)/((-2)^(x+1)+3^(x+1) )