\(\Leftrightarrow\left(x-1\right)^2=576\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=24\\x-1=-24\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=25\\x=-23\end{matrix}\right.\)
\(\dfrac{x-1}{6^2}=\dfrac{4^2}{x-1}\left(x\ne1\right).\)
\(\Leftrightarrow\dfrac{x-1}{36}=\dfrac{16}{x-1}.\Rightarrow\left(x-1\right)^2=576.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^2=24^2.\\\left(x-1\right)^2=\left(-24\right)^2.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=24.\\x-1=-24.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=25.\\x=-23.\end{matrix}\right.\)(TM).