Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$ I am to find the limit of 
$$\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$$ 
so I used:
$$\lim_{x \to -\infty} = \lim_{x \to \infty}f(-x)$$ 
but I just can't solve it to the end.

$\lim_{x \to -\infty} \left(\dfrac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)
=\lim_{x \to -\infty} \left(\dfrac{3^{-x}(4^{x+2}\cdot3^x- 2)}{3^{-x}(4^{-x}\cdot3^x+2\cdot3^{2x+1})}\right)
=\lim_{x \to -\infty} \left(\dfrac{4^{x+2}\cdot3^x- 2}{(3/4)^x+2\cdot3^{2x+1}}\right)$
The numerator converges to $-2$ while the denominator diverges to $\infty$, and so the limit is $0$.
