a) `(x\sqrt{x}+y\sqrt{y})/(\sqrt{x}+\sqrt{y})-\sqrt{xy}` `(x,y>=0,xney)`
`=((\sqrt{x})^3+(\sqrt{y})^3)/(\sqrt{x}+\sqrt{y})`
`=((\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y))/(\sqrt{x}+\sqrt{y})-\sqrt{xy}`
`=x-\sqrt{xy}+y-\sqrt{xy}`
`=x-2\sqrt{xy}+y`
`=(\sqrt{x}-\sqrt{y})^2`