\(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}< \dfrac{2}{3}\\ \Leftrightarrow\dfrac{3\sqrt{x}-3}{3\left(\sqrt{x}+1\right)}< \dfrac{2\sqrt{x}-2}{3\left(\sqrt{x}+1\right)}\\ \Rightarrow3\sqrt{x}-3< 2\sqrt{x}-2\\ \Leftrightarrow\sqrt{x}< 1\\ \Rightarrow\left\{{}\begin{matrix}x< 1\\x\ge0\end{matrix}\right.\Rightarrow x\le0< 1\)