transforming a specific equation

Question

how does the following equation:

$$\frac{1}{\sqrt{1+z^2}-z}$$

get transformed into:

$$\sqrt{1+z^2}+z$$

I'm sure I'm missing something obvious. Thanks.

Answer 1

$$\frac1{\sqrt{1+z^2}-z} = \frac{\sqrt{1+z^2}+z}{(\sqrt{1+z^2}-z)(\sqrt{1+z^2}+z)} = \frac{\sqrt{1+z^2}+z}{(1+z^2)-(z^2)} = \sqrt{1+z^2}+z$$