\(P=A.B=\dfrac{\sqrt x+1}{\sqrt x-1}.\dfrac{\sqrt x}{\sqrt x+1}\\=\dfrac{\sqrt x}{\sqrt x-1}\\=\dfrac{\sqrt x-1+1}{\sqrt x-1}\\=1+\dfrac{1}{\sqrt x-1}\)
Vì \(\sqrt x\ge 0\\→\sqrt x-1\ge -1\\→\dfrac{1}{\sqrt x-1}\le -1\\→P≤1-1=0\\→\max P=0\)
\(→\) Dấu "=" xảy ra khi \(\sqrt x=0(TM)\)
\(↔x=0\)
Vậy \(\max P=0\) khi \(x=0\)