\(a,x=16\Leftrightarrow A=\dfrac{16+3}{4+3}=\dfrac{19}{7}\\ b,B=\dfrac{x+3\sqrt{x}-2-\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\\ B=\dfrac{x+2\sqrt{x}+1}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\\ B=\dfrac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\\ c,P=\dfrac{A}{B}=\dfrac{x+3}{\sqrt{x}+3}\cdot\dfrac{\sqrt{x}+3}{\sqrt{x}+1}=\dfrac{x+3}{\sqrt{x}+1}\\ P=\dfrac{x-1+4}{\sqrt{x}+1}=\sqrt{x}-1+\dfrac{4}{\sqrt{x}+1}=\sqrt{x}+1+\dfrac{4}{\sqrt{x}+1}-2\\ P\ge2\sqrt{4}+2=6\\ P_{min}=6\Leftrightarrow\sqrt{x}+1=2\Leftrightarrow x=1\left(tm\right)\)
