a: Ta có: \(P=\left(\dfrac{x+2\sqrt{x}-7}{x-9}-\dfrac{\sqrt{x}-1}{\sqrt{x}-3}\right):\left(\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-1}\right)\)
\(=\dfrac{x+2\sqrt{x}-7-x-2\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\sqrt{x}-1-\sqrt{x}-3}\)
\(=\dfrac{-4\left(\sqrt{x}-1\right)}{-4\left(\sqrt{x}-3\right)}\)
\(=\dfrac{\sqrt{x}-1}{\sqrt{x}-3}\)
d: Để P nguyên thì \(\sqrt{x}-3\in\left\{-2;-1;1;2\right\}\)
\(\Leftrightarrow\sqrt{x}\in\left\{2;4;5\right\}\)
hay \(x\in\left\{4;16;25\right\}\)
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