how we can calculate $ \frac {\sqrt {x^2} + \sqrt {y^2} }{2 \sqrt {xyz}}$? I teach math for Schools. How can Help me in the following past Olympiad question?

If $y,z$ be two negative distinct number and $x$ and $y$ be negate of each other, how we can calculate $ \displaystyle\frac {\sqrt {x^2} + \sqrt {y^2} }{2 \sqrt {xyz}}$? 
1) $\frac {\sqrt{x}}{x}$
2)$\frac {\sqrt{-y}}{y}$
3) $\frac {\sqrt{z}}{z}$
4) $\frac {\sqrt{-z}}{-z}$


$$\frac{\sqrt{x^2}+\sqrt{y^2}}{2\sqrt{xyz}}=\frac{2\sqrt{x^2}}{2\sqrt{-x^2z}}$$ using $y=-x$. This yields: $$\frac{2\sqrt{x^2}}{2\sqrt{x^2}\sqrt{-z}}=\frac{1}{\sqrt{-z}}$$. Note that $z<0$, so $-z>0$, so $\sqrt{-z}$ is well-defined.
