I'm reviewing Algebra in an attempt to review Calculus and came upon a question in the Algebra Diagnostic that asked to rationalize an expression and simplify.

To my understanding, rationalization is the process of rewriting a given expression so that the denominator is non-zero. The equation is, thus:

$$\frac{\sqrt{4+h} - 2}{h}$$

I understand that $h$ can equal zero, and therefore cannot be in the denominator. The answer given is:

$$\frac{1}{\sqrt{4+h} + 2}$$

The denominator in the answer, I believe, is the conjugate of the numerator in the question, but how did they arrive at this state? And in general, is my understanding of rationalization flawed? What is the point and how will that be applied at higher levels of math?

Thank you