a) tự làm.
b) \(P=\left(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}-\dfrac{x\sqrt{x}-y\sqrt{y}}{x-y}\right)\div\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
\(=\left(\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}-\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\right)\cdot\dfrac{\sqrt{x}+\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}\)
\(=\left(\sqrt{x}+\sqrt{y}-\dfrac{x+\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\right)\cdot\dfrac{\sqrt{x}+\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)+\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)-\left(x+\sqrt{xy}+y\right)}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{\sqrt{x}+\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}\)
\(=\dfrac{x+\sqrt{xy}+\sqrt{xy}+y-x-\sqrt{xy}-y}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{\sqrt{x}+\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}\)
\(=\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{\sqrt{x}+\sqrt{y}}{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}\)
\(=\sqrt{xy}\cdot\dfrac{1}{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}\)
\(=\dfrac{\sqrt{xy}}{x-2\sqrt{xy}+y+\sqrt{xy}}\)
\(=\dfrac{\sqrt{xy}}{x-\sqrt{xy}+y}\)
