# Math Help - Hard limit problem

1. ## Hard limit problem

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) )

2. That is just $\displaystyle \lim _{x \to - \infty } \frac{{1 + \left( {\frac{{ - 2}}
{3}} \right)^{ - x} }}
{{ - 2 + 3\left( {\frac{{ - 2}}
{3}} \right)^{ - x} }}$