\(Q=\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\left(\dfrac{x-y}{\sqrt{x}-\sqrt[]{y}}+\dfrac{x\sqrt{x}-y\sqrt{y}}{y-x}\right)\)
\(=\dfrac{x+y-2\sqrt{xy}+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\left(\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}-\dfrac{\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right)\)
\(=\dfrac{x+y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\left(\sqrt{x}+\sqrt{y}-\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+y+\sqrt{xy}\right)}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right)\)
\(=\dfrac{x+y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\dfrac{\left(\sqrt{x}+\sqrt{y}\right)^2-x-y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
\(=\dfrac{x+y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\dfrac{x+y+2\sqrt{xy}-x-y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}=\dfrac{x+y-\sqrt{xy}}{\sqrt{xy}}\)
\(Q=\dfrac{x-2\sqrt{xy}+y+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\left(\dfrac{\left(x-y\right)\left(\sqrt{x}+\sqrt{y}\right)-x\sqrt{x}+y\sqrt{y}}{x-y}\right)\)
\(=\dfrac{x-\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{x-y}{x\sqrt{x}+x\sqrt{y}-y\sqrt{x}-y\sqrt{y}-x\sqrt{x}+y\sqrt{y}}\)
\(=\dfrac{x-\sqrt{xy}+y}{1}\cdot\dfrac{\sqrt{x}-\sqrt{y}}{x\sqrt{y}-y\sqrt{x}}\)
\(=\dfrac{x-\sqrt{xy}+y}{1}\cdot\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}=\dfrac{x-\sqrt{xy}+y}{\sqrt{xy}}\)