\(1,A=\dfrac{2\cdot5-1}{5-3}=\dfrac{9}{2}\\ 2,B=\dfrac{2x+3\sqrt{x}+9-x+3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\\ B=\dfrac{x+6\sqrt{x}+9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}+3}{\sqrt{x}-3}\\ 3,P=\dfrac{A}{B}=\dfrac{2\sqrt{x}-1}{\sqrt{x}-3}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}+3}=\dfrac{2\sqrt{x}-1}{\sqrt{x}+3}=\dfrac{2\left(\sqrt{x}+3\right)-5}{\sqrt{x}+5}\\ P=2-\dfrac{5}{\sqrt{x}+3}\ge2-\dfrac{5}{0+3}=2-\dfrac{5}{3}=\dfrac{1}{3}\\ P_{min}=\dfrac{1}{3}\Leftrightarrow x=0\)
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