Question

[Cao Lê Trúc Phương]

\(\dfrac{\sqrt{27}-\sqrt{15}}{3-\sqrt{5}}+\dfrac{4}{2+\sqrt{3}}-\dfrac{6}{\sqrt{3}}\)

\(\dfrac{x-y}{\sqrt{x}+\sqrt{y}}-\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}\)

Answer 1

[2611]

`[\sqrt{27}-\sqrt{15}]/[3-\sqrt{5}]+4/[2+\sqrt{3}]-6/\sqrt{3}`

`=[\sqrt{3}(3-\sqrt{5})]/[3-\sqrt{5}]+[4(2-\sqrt{3})]/[4-3]-[2\sqrt{3}.\sqrt{3}]/\sqrt{3}`

`=\sqrt{3}+8-4\sqrt{3}-2\sqrt{3}`

`=8-5\sqrt{3}`

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`[x-y]/[\sqrt{x}+\sqrt{y}]-[x\sqrt{y}+y\sqrt{x}]/\sqrt{xy}`    `ĐK:  x,y > 0`

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

`=\sqrt{x}-\sqrt{y}-\sqrt{x}-\sqrt{y}`

`=-2\sqrt{y}`