First, let me break up each quantity:

Quantity A:

$\frac{2}{x}+\frac{x}{x}-\frac{x^{2}}{x} = \frac{2}{x}+1-x$

Quantity B:

$\frac{2y^{2}}{y}+\frac{y}{y}-\frac{1}{y} = 2y+1- \frac{1}{y}$

Now subtract 1 from each quantity:

Quantity A: $\frac{2}{x}-x$

Quantity B: $2y - \frac{1}{y}$

Now we need some intuitive mathematical thinking. What if, instead of $x < \frac{1}{y}$, we had $x = \frac{1}{y}$? In that case, both quantities would be equal. Quantity A would become $\frac{2}{\frac{1}{y}} - \frac{1}{y} = 2y - \frac{1}{y}$, same as quantity B.

In reality, though, x is a bit less than $\frac{1}{y}$. What happens when x gets smaller? Well, when x decreases, $\frac{2}{x}$ increases, while the number we subtract, x, decreases. So when x gets smaller, quantity A gets larger.

Putting it all together, if x was equal to $\frac{1}{y}$, then both quantities would be equal. But x is actually a bit less than that, and as x decreases, quantity A increases while quantity B stays the same. Hence, quantity A is larger, no matter what.