1.
\(P=\dfrac{3}{\sqrt{x}+3}\le\dfrac{3}{0+3}=1\)
\(\Rightarrow maxP=1\Leftrightarrow x=0\)
2.
\(A=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}=\dfrac{2\left(\sqrt{x}+1\right)-3}{\sqrt{x}+1}=2-\dfrac{3}{\sqrt{x}+1}\ge2-\dfrac{3}{0+1}=-1\)
\(\Rightarrow minA=-1\Leftrightarrow x=0\)