#andy
\[\begin{array}{l}
\frac{{a + 1 + \sqrt a }}{{\sqrt a \, - 1}} > 1\\
\Leftrightarrow \frac{{a + 1 + \sqrt a - \sqrt {a\,} + 1}}{{\sqrt a - 1}}\,;\,dk:a \ge 0,\,a \ne 1\\
\Leftrightarrow \frac{{a + 2}}{{\sqrt a - 1}} > 1\\
\Leftrightarrow \sqrt a - 1 > 0\\
\Rightarrow a > 1
\end{array}\]