What facts are used implicitly to make the following deductions?

$\frac{x+2}{y} < 4x+1$

$\Rightarrow \frac{y}{x+2} > \frac{1}{4x+1}$

$\Rightarrow \frac{y^2}{(x+2)^2} > \frac{1}{(4x+1)^2} > \frac{1}{4x+1}$