ĐKXĐ: x>0 và y>0
Sửa đề: \(A=\left(x-\dfrac{\sqrt{xy^2}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}\right)\left(\dfrac{\sqrt{y}}{\sqrt{xy}+y}-\dfrac{\sqrt{x}}{\sqrt{xy}-x}+\dfrac{\sqrt{y}}{x-y}\right)\)
\(=\left(x-\dfrac{y\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+\sqrt{y}}\right)\left(\dfrac{\sqrt{y}}{\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)}-\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{y}-\sqrt{x}\right)}+\dfrac{\sqrt{y}}{x-y}\right)\)
\(=\left(x-y\right)\cdot\left(\dfrac{1}{\sqrt{x}+\sqrt{y}}+\dfrac{1}{\sqrt{x}-\sqrt{y}}+\dfrac{\sqrt{y}}{x-y}\right)\)
\(=\left(x-y\right)\cdot\dfrac{\sqrt{x}-\sqrt{y}+\sqrt{x}+\sqrt{y}+\sqrt{y}}{x-y}\)
\(=2\sqrt{x}+\sqrt{y}\)
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