\(a,P=\left(\dfrac{2\sqrt{xy}}{x-y}-\dfrac{\sqrt{x}+\sqrt{y}}{2\sqrt{x}-2\sqrt{y}}\right)\cdot\dfrac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\left(x,y\ge0;x\ne y\right)\\ P=\dfrac{4\sqrt{xy}-\left(\sqrt{x}+\sqrt{y}\right)^2}{2\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\cdot\dfrac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\\ P=\dfrac{-x+2\sqrt{xy}-y}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\cdot\dfrac{\sqrt{x}}{\sqrt{x}-\sqrt{y}}\\ P=\dfrac{-\left(\sqrt{x}-\sqrt{y}\right)^2}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\cdot\dfrac{\sqrt{x}}{\sqrt{x}-\sqrt{y}}\\ P=\dfrac{-\sqrt{x}}{\sqrt{x}+\sqrt{y}}\)
\(b,\dfrac{x}{y}=\dfrac{4}{9}\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{y}}=\dfrac{2}{3}\Leftrightarrow\sqrt{x}=\dfrac{2}{3}\sqrt{y}\\ P=-\dfrac{2}{3}\sqrt{y}:\left(\dfrac{2}{3}\sqrt{y}+\sqrt{y}\right)=\dfrac{-2\sqrt{y}}{3}:\dfrac{5\sqrt{y}}{3}=-\dfrac{2\sqrt{y}}{3}\cdot\dfrac{3}{5\sqrt{y}}=-\dfrac{2}{5}\)