Rationalize the numerator of each of the following expressions √a - 2 / a -4 the answer is supposed to be 1 / √a + 2 Please show me the steps of how you got this answer please

So $a - 4 = (\sqrt a - 2)(\sqrt a + 2)$, giving you a fraction of

$$ \frac{\sqrt a - 2}{ (\sqrt a - 2)(\sqrt a + 2)} = \frac{1}{\sqrt a + 2}$$ as desired.

This turns out to be a problem where you recognize that the denominator can be factored by something in the numerator - basically it's a pattern recognition problem.