How to rationalize $(\sqrt{4 + h} - 2) / h$?

Question

How to rationalize this? $$\frac{\sqrt{4 + h} - 2} h$$

I tried multiplying it by $$\frac{\sqrt{4 + h} + 2}{\sqrt{4 + h} + 2}$$ but I could not get the correct answer.

The correct answer is $\frac{1}{\sqrt{4 + h} + 2}$.

Answer 1

When you foil out $(\sqrt{4+h}-2)(\sqrt{4+h}+2)$ the "inner and outer" terms cancel and you have $4+h-4=h.$

So after the division by $h$ in the given expression it becomes the answer you quote.

Answer 2

Doesn't rationalizing usually go in the reverse direction? Anyway, you get from point a to point b as follows: $$ \frac{1}{\sqrt{4+h}+2}=\frac{1}{\sqrt{4+h}+2}\cdot\frac{\sqrt{4+h}-2}{\sqrt{4+h}-2}=\frac{\sqrt{4+h}-2}{h} $$