\(\begin{array}{l}
Q = \frac{{\sqrt x + 1}}{{\sqrt x - 1}} = \frac{{\sqrt x - 1 + 2}}{{\sqrt x - 1}} = 1 + \frac{2}{{\sqrt x - 1}}\,\left( {x \ge 0;x \ne 1} \right)\\
Q \in Z \Rightarrow \frac{2}{{\sqrt x - 1}} \in Z \Rightarrow \left( {\sqrt x - 1} \right) \in U\left( 2 \right) = \left\{ { \pm 1; \pm 2} \right\}\\
+ )\,\sqrt x - 1 = - 1 \Leftrightarrow \sqrt x = 0 \Leftrightarrow x = 0\left( {tm} \right)\\
+ )\,\sqrt x - 1 = 1 \Leftrightarrow \sqrt x = 2 \Leftrightarrow x = 4\left( {tm} \right)\\
+ )\,\sqrt x - 1 = - 2 \Leftrightarrow \sqrt x = - 1\left( {VL} \right)\\
+ )\,\sqrt x - 1 = 2 \Leftrightarrow \sqrt x = 3 \Leftrightarrow x = 9\left( {tm} \right)
\end{array}\)
