Đáp án:
`P=(-x\sqrt{y}-y\sqrt{x})/(x-y)`
Giải thích các bước giải:
`P=(x-y)/(\sqrt{x}+\sqrt{y}) - (\sqrt{x^3} + \sqrt{y^3})/(x-y)`
`=((x-y)(\sqrt{x}-\sqrt{y}))/((\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y}))-((\sqrt{x})^3+(\sqrt{y})^3)/(x-y)`
`=((x-y)(\sqrt{x}-\sqrt{y}))/((\sqrt{x})^2-(\sqrt{y})^2)-((\sqrt{x}+\sqrt{y})[(\sqrt{x})^2-\sqrt{x}\sqrt{y}+(\sqrt{y})^2])/(x-y)`
`=((x-y)(\sqrt{x}-\sqrt{y}))/(x-y)-((\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y))/(x-y)`
`=((x-y)(\sqrt{x}-\sqrt{y})-[(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)])/(x-y)`
`=((x\sqrt{x}-x\sqrt{y}-y\sqrt{x}+y\sqrt{y})-(x\sqrt{x}-x\sqrt{y}+y\sqrt{x}+x\sqrt{y}-y\sqrt{x}+y\sqrt{y}))/(x-y)`
`=(x\sqrt{x}-x\sqrt{y}-y\sqrt{x}+y\sqrt{y}-x\sqrt{x}+x\sqrt{y}-y\sqrt{x}-x\sqrt{y}+y\sqrt{x}-y\sqrt{y})/(x-y)`
`=(-x\sqrt{y}-y\sqrt{x})/(x-y)`
Vậy `P =(-x\sqrt{y}-y\sqrt{x})/(x-y)`
