$\mathrm{f}(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0$ is stricity decreasing in

To determine where the function $f(x) = \frac{x}{2} + \frac{2}{x}$ is strictly decreasing, we analyze its derivative, $f'(x) = \frac{1}{2} - \frac{2}{x^2}$, and solve $f'(x) < 0$.

$\frac{1}{2} - \frac{2}{x^2} < 0$ implies $\frac{1}{2} < \frac{2}{x^2}$, and multiplying both sides by $2x^2$ (positive for $x \neq 0$) gives $x^2 < 4$, so $|x| < 2$.

Considering the domain $x \neq 0$, $f(x)$ is strictly decreasing on $(-2, 0)$ and $(0, 2)$.

Option C, $(-2, 2)$, represents the union of these intervals, excluding the discontinuity at $x = 0$, and is the correct choice.