\[\boxed{\text{197\ (197).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\frac{6x}{(x - 1)(x - 2)} = \frac{a^{\backslash x - 2}}{x - 1} + \frac{b^{\backslash x - 1}}{x - 2}\]
\[Преобразуем\ правую\ часть\ \]
\[равенства:\]
\[6x = ax - 2a + bx - b\]
\[6x + 0 = x(a + b) + ( - 2a - b)\]
\[\left\{ \begin{matrix} a + b = 6\ \ \ \ \ \ \\ - 2a - b = 0 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} a = 6 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 2(6 - b) - b = 0 \\ \end{matrix} \right.\ \]
\[- 2(6 - b) - b = 0\]
\[- 12 + 2b - b = 0\]
\[- 12 + b = 0\]
\[b = 12;\]
\[a = 6 - b = 6 - 12 = - 6.\]
\[Тождественны\ при\ \]
\[a = - 6,\ b = 12.\]
\[Ответ:\ при\ a = - 6;b = 12.\]