Đáp án:

Giải thích các bước giải:

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

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

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

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

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

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

Đáp án+Giải thích các bước giải:

 Với `x,y >= 0,x \ne y`.Ta có:

     `M=\frac{x+x\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\frac{x-y}{\sqrt{x}-\sqrt{y}}`

     `M=\frac{x+x\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\frac{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}{\sqrt{x}-\sqrt{y}}`

     `M=\frac{x+x\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}+\sqrt{y})`

     `M=\frac{x+x\sqrt{y}-(\sqrt{x}+\sqrt{y})^2}{\sqrt{x}+\sqrt{y}}`

     `M=\frac{x+x\sqrt{y}-(x+2\sqrt{x}\sqrt{y}+y)}{\sqrt{x}+\sqrt{y}}`

     `M=\frac{x+x\sqrt{y}-x-2\sqrt{xy}-y}{\sqrt{x}+\sqrt{y}}`

     `M=\frac{x\sqrt{y}-2\sqrt{xy}-y}{\sqrt{x}+\sqrt{y}}`