The problem at hand:
$$\lim_{x\to1}\frac{4^x-4}{2^x-2}=?$$
I know this problem could be easily done with L'Hopital's rule but I was wondering what the optimal solution would be to get rid of the discontinuity at $x=1$ without invoking the rule? I tried all sorts of algebraic manipulations to no avail so any input would be greatly appreciated! Thank you.
HINT
Use $a^2-b^2=(a-b)(a+b)$ that is
$$4^x-4=2^{2x}-2^2=(2^x-2)(2^x+2)$$