\(ĐKXĐ:x\ge0\)
\(\dfrac{\sqrt{x}+1}{\sqrt{x}}>\dfrac{2}{3}\Leftrightarrow\dfrac{3\sqrt{x}+3}{3\sqrt{x}}>\dfrac{2\sqrt{x}}{3\sqrt{x}}\)
\(\Rightarrow3\sqrt{x}-2\sqrt{x}>-3\)
\(\Leftrightarrow\sqrt{x}>-3\)
\(\Leftrightarrow\left[{}\begin{matrix}0< x< 9\\x>9\end{matrix}\right.\)
mà \(x\in \mathbb Z\) \(\Rightarrow x\in \mathbb N \), \(x\ne9\).