Với \(x>0\) ta có:
\(\Leftrightarrow\frac{\sqrt{x}\left(x-\sqrt{x}-2\right)}{\left(\sqrt{x}+1\right)\left(x+2\sqrt{x}-5\right)}>0\)
\(\Leftrightarrow\frac{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+1\right)\left(x+2\sqrt{x}-5\right)}>0\)
\(\Leftrightarrow\frac{\sqrt{x}-2}{x+2\sqrt{x}-5}>0\)
\(\Leftrightarrow\frac{\sqrt{x}-2}{\left(\sqrt{x}+1+\sqrt{6}\right)\left(\sqrt{x}+1-\sqrt{6}\right)}>0\)
\(\Leftrightarrow\frac{\sqrt{x}-2}{\sqrt{x}+1-\sqrt{6}}>0\)
\(\Rightarrow\left[{}\begin{matrix}0< \sqrt{x}< \sqrt{6}-1\\\sqrt{x}>2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}0< x< 7-2\sqrt{6}\\x>4\end{matrix}\right.\)
