I have a question about the following inequality:
$a - \frac{2}{a} + 1 > 0$
This is obviously a polynomial of the second degree.
Is this the simplest way of solving the given equation?
$\frac{a}{a} * (a - \frac{2}{a} + 1 > 0) > 0$
$\frac{a^2 - 2 + a}{a}>0$
$\frac{(a-1)(a+2)}{a}>0$
$a \in (-2,0) \cup (1, +\infty)$
... or is there a faster/mathematically "cleaner" way of doing it?
Thanks in advance.