\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)\left(y^2+1\right)+\left(y-2\right)=0\\\left(y-2\right)\left(x^2+1\right)=x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(y-2\right)\left(x^2+1\right)\left(y^2+1\right)+\left(y-2\right)=0\\\left(y-2\right)\left(x^2+1\right)=x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(y-2\right)\left(\left(x^2+1\right)\left(y^2+1\right)+1\right)=0\\\left(y-2\right)\left(x^2+1\right)=x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}y=2\\\left(x^2+1\right)\left(y^2+1\right)+1=0\left(vl\right)\end{matrix}\right.\\\left(y-2\right)\left(x^2+1\right)=x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=2\\\left(2-2\right)\left(x^2+1\right)=x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=1\end{matrix}\right.\)
