ĐKXĐ: \(x\ge\frac{1}{3}\)
\(\Leftrightarrow3x-x\sqrt{3x-1}=\sqrt{\left(3x-1\right)\left(x+1\right)}-x\sqrt{x+1}+1\)
\(\Leftrightarrow3x-1-\sqrt{\left(3x-1\right)\left(x+1\right)}-x\left(\sqrt{3x-1}-\sqrt{x+1}\right)=0\)
\(\Leftrightarrow\sqrt{3x-1}\left(\sqrt{3x-1}-\sqrt{x+1}\right)-x\left(\sqrt{3x-1}-\sqrt{x+1}\right)=0\)
\(\Leftrightarrow\left(\sqrt{3x-1}-x\right)\left(\sqrt{3x-1}-\sqrt{x+1}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{3x-1}=x\\\sqrt{3x-1}=\sqrt{x+1}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=x^2\\3x-1=x+1\end{matrix}\right.\)
\(\Leftrightarrow...\)