a: Ta có: \(M=\left(\dfrac{3\sqrt{x}}{x+\sqrt{xy}+y}-\dfrac{3x}{x\sqrt{x}-y\sqrt{y}}+\dfrac{1}{\sqrt{x}-\sqrt{y}}\right):\dfrac{\left(x-1\right)\left(\sqrt{x}-\sqrt{y}\right)}{2x+2\sqrt{xy}+2y}\)
\(=\dfrac{3x-3\sqrt{xy}-3x+x+\sqrt{xy}+y}{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}\cdot\dfrac{2\left(x+\sqrt{xy}+y\right)}{\left(x-1\right)\left(\sqrt{x}-\sqrt{y}\right)}\)
\(=\dfrac{x-2\sqrt{xy}+y}{\sqrt{x}-\sqrt{y}}\cdot\dfrac{1}{\left(x-1\right)\left(\sqrt{x}-\sqrt{y}\right)}\)
\(=\dfrac{1}{x-1}\)
b: Để M nguyên thì \(x-1\in\left\{1;-1\right\}\)
hay \(x\in\left\{2;0\right\}\)
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