\(A=\dfrac{9+\left(2\sqrt{x}+5\right)\left(\sqrt{x}-2\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\\ A=\dfrac{9+2x+\sqrt{x}-10-x+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}-2}\\ A=\dfrac{\sqrt{x}}{\sqrt{x}-2}=1+\dfrac{2}{\sqrt{x}-2}\in Z\\ \Leftrightarrow\sqrt{x}-2\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\\ \Leftrightarrow\sqrt{x}\in\left\{0;1;3;4\right\}\\ \Leftrightarrow x\in\left\{0;1;9;16\right\}\)
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