ĐK: \(x\ge0\)
Lấy P - 1
\(\dfrac{\sqrt{x}-2}{2\sqrt{x}+1}-1\)
\(=\dfrac{\sqrt{x}-2-2\sqrt{x}-1}{2\sqrt{x}+1}\)
\(=\dfrac{-\sqrt{x}-3}{2\sqrt{x}+1}\)
\(=\dfrac{-\left(\sqrt{x}+3\right)}{2\sqrt{x}+1}\)
Ta thấy \(\left\{{}\begin{matrix}\sqrt{x}+3>0\\2\sqrt{x}+1>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}-\left(\sqrt{x}+3\right)< 0\\2\sqrt{x}+1>0\end{matrix}\right.\Rightarrow P-1< 0\)
Vậy \(P< 1\).