ĐKXĐ: \(x\ge1\)
\(\Leftrightarrow2\sqrt{\left(x-1\right)\left(x+5\right)}+\left(x+1\right)\sqrt{x+5}=\left(x+5\right)+2\left(x+1\right)\sqrt{x-1}\)
\(\Leftrightarrow\sqrt{x+5}\left(2\sqrt{x-1}-\sqrt{x+5}\right)-\left(x+1\right)\left(2\sqrt{x-1}-\sqrt{x+5}\right)=0\)
\(\Leftrightarrow\left(\sqrt{x+5}-x-1\right)\left(2\sqrt{x-1}-\sqrt{x+5}\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+5}=x+1\\2\sqrt{x-1}=\sqrt{x+5}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+5=x^2+2x+1\\4\left(x-1\right)=x+5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+x-4=0\\3x=9\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{-1+\sqrt{17}}{2}\\x=\frac{-1-\sqrt{17}}{2}\left(l\right)\\x=3\end{matrix}\right.\)
