1. Simplify the fraction $\frac{\sqrt{-x}-\sqrt{-3 y}}{x+3 y+2 \sqrt{3 x y}}$.

Answer. $\frac{1}{\sqrt{-3 y}-\sqrt{-x}}$.
Let $-x=u,-y=v$, where $u \geq 0, v \geq 0$. Then the given fraction is equal to $\frac{\sqrt{u}-\sqrt{3 v}}{-u-3 v+2 \sqrt{3 u v}}=\frac{\sqrt{u}-\sqrt{3 v}}{-(\sqrt{u}-\sqrt{3 v})^{2}}=\frac{1}{\sqrt{3 v}-\sqrt{u}}=\frac{1}{\sqrt{-3 y}-\sqrt{-x}}$.