Đáp án+Giải thích các bước giải:
`b)(x>0;y>0;x\ney)`
Xét Vế trái:
`((\sqrt{y})/(x-\sqrt{xy})+(\sqrt{x})/(y-\sqrt{xy})):(\sqrt{x}+\sqrt{y})/(\sqrt{xy})`
`=((\sqrt{y})/(x-\sqrt{xy})-(\sqrt{x})/(\sqrt{xy}-y)):(\sqrt{x}+\sqrt{y})/(\sqrt{xy})`
`=((\sqrt{y})/(\sqrt{x}(\sqrt{x}-\sqrt{y}))-(\sqrt{x})/(\sqrt{y}.(\sqrt{x}-\sqrt{y}))):(\sqrt{x}+\sqrt{y})/(\sqrt{xy})`
`=((y)/(\sqrt{xy}(\sqrt{x}-\sqrt{y}))-(x)/(\sqrt{xy}.(\sqrt{x}-\sqrt{y}))).(\sqrt{xy})/(\sqrt{x}+\sqrt{y})`
`=(-(x-y))/(\sqrt{xy}(\sqrt{x}-\sqrt{y})).(\sqrt{xy})/(\sqrt{x}+\sqrt{y})`
`=(-(\sqrt{x}-\sqrt{y}).(\sqrt{x}+\sqrt{y}))/((\sqrt{x}-\sqrt{y}).(\sqrt{x}+\sqrt{y}))`
`=-1`
`=` Vế phải(đpcm)
Vậy `((\sqrt{y})/(x-\sqrt{xy})+(\sqrt{x})/(y-\sqrt{xy})):(\sqrt{x}+\sqrt{y})/(\sqrt{xy})=-1`
