\[(m - 1)x^{2} - 2(m + 1)x + m - 3 = 0.\]
\[4(6m - 2) > 0\]
\[6m - 2 > 0\]
\[6m > 2\]
\[m > \frac{1}{3}.\]
\[2)\ Становится\ линейным:\]
\[m - 1 = 0\]
\[m = 1.\]
\[Ответ:\ \ m = 2.\]