
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) )

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