I have been studying independently through various online courses and I still have trouble understanding what to do with certain limits. I am hoping for some guidance on the following two problems to help me solve them (I do not need to answer as much as help understanding where I am going).

$$ \lim\_{x\to 0} \frac{\sqrt{16 + 4x} - \sqrt{16 - 4x}}{x} $$

$$ \lim\_{x\to 0} \frac{\frac{1}{(x + 6)^2} - \frac{1}{36}}{x} $$

I can tell that these are both $ \frac{0}{0} $ indeterminate equations and I can simplify them in a number of ways but I cannot seem to get the 0 out of the bottom of the equation. Any help pointing me in the right direction would be greatly appreciated!