The expression is determined with all \(x\in R\)

\(\Leftrightarrow x^2+1+3x-x\sqrt{x^2+1}-3\sqrt{x^2+1}=0\)

\(\Leftrightarrow\left(x^2+1\right)^2-x\sqrt{x^2+1}+3x-3\sqrt{x^2+1}=0\)

\(\Leftrightarrow\sqrt{x^2+1}\left(\sqrt{x^2+1}-x\right)-3\left(\sqrt{x^2+1}-x\right)=0\)

\(\Leftrightarrow\left(\sqrt{x^2+1}-x\right)\left(\sqrt{x^2+1}-3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x^2+1}=x\left(not-satisfy\right)\\\sqrt{x^2+1}=3\end{matrix}\right.\Leftrightarrow x=\pm2\sqrt{2}\)