This probably involves some very easy algebra, but I am stuck and would appreciate some help. Walter Rudin's Example 1.1 on page 2 of Principles of Mathematical Analysis includes the following observation:
If $p > 0$ and $q = p - \dfrac{p^2 - 2}{p + 2} = \dfrac{2p + 2}{p + 2}$ then
If $p^2 - 2 > 0$ this implies $0 < q < p$.
I can see how $q < p$, but why is $q$ (necessarily) $> 0$?
I'm sure I am missing something obvious.