`~rai~`
\(\dfrac{(\sqrt{x}+\sqrt{y})^2}{x\sqrt{y}+y\sqrt{x}}\\=\dfrac{(\sqrt{x}+\sqrt{y})^2}{\sqrt{xy}(\sqrt{x}+\sqrt{y})}\\=\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{xy}}\\=\dfrac{\sqrt{xy}(\sqrt{x}+\sqrt{y})}{\sqrt{xy}.\sqrt{xy}}\\=\dfrac{x\sqrt{y}+y\sqrt{x}}{xy}.\)