x^2 +xy...

denisabramov257 @denisabramov257

July 2022 1 7 Report

(√x/√x-√y - √y/√x+√y) * x-y /x^2 +xy

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$\Big(\dfrac{\sqrt{x} }{\sqrt{x} -\sqrt{y} } -\dfrac{\sqrt{y} }{\sqrt{x} +\sqrt{y} } \Big)\cdot\dfrac{x-y}{x^{2} +xy} =\\\\\\=\dfrac{\sqrt{x} (\sqrt{x} +\sqrt{y})-\sqrt{y} (\sqrt{x} -\sqrt{y}) }{(\sqrt{x} -\sqrt{y} )(\sqrt{x} +\sqrt{y} )} \cdot\dfrac{x-y}{x(x+y)} =\\\\\\=\dfrac{x+\sqrt{xy} -\sqrt{xy} +y}{x-y} \cdot\dfrac{x-y}{x(x+y)} =\dfrac{x+y}{x-y}\cdot\dfrac{x-y}{x(x+y)} =\boxed{\dfrac{1}{x} }$

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