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$\lim_{x \to 2} \frac{3^x + 3^{3-x} - 12}{3^{-x/2} - 3^{1-x}}$ is equal to ______.
Let $3^x = t^2$. $\lim_{t\to 3}\frac{t^2 + 27/t^2 - 12}{1/t - 3/t^2} = \lim_{t\to 3}\frac{t^4 - 12t^2 + 27}{t - 3} = \lim_{t\to 3}\frac{(t^2-3)(t+3)(t-3)}{t-3} = (9-3)(3+3) = 36$.
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