Question

Giải chi tiết cho mình với ạ

Answer 1

`4)` Với `x \ne y;x,y >= 0` có:

`[x+\sqrt{y}+y\sqrt{x}]/[x\sqrt{y}-y\sqrt{x}]:[x-y]/[\sqrt{x}-\sqrt{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}]/[\sqrt{x}-\sqrt{y}]. 1/[\sqrt{x}+\sqrt{y}]`

`=1/[\sqrt{x}-\sqrt{y}]`

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`5)` Với `x \ne y;x,y >= 0` có:

  `[(\sqrt{x}+\sqrt{y})^2-4\sqrt{xy}]/[\sqrt{x}-\sqrt{y}]`

`=[x+2\sqrt{xy}+y-4\sqrt{xy}]/[\sqrt{x}-\sqrt{y}]`

`=[x-2\sqrt{xy}+y]/[\sqrt{x}-\sqrt{y}]`

`=[(\sqrt{x}-\sqrt{y})^2]/[\sqrt{x}-\sqrt{y}]=\sqrt{x}-\sqrt{y}`

Answer 2