Для каждого значения а решите уравнение: (x^2-(a+3)x+3a)/(x-1)=0.

\[x^{2} - (a + 3)x + 3a = 0\]

\[D = (a + 3)^{2} - 4 \cdot 1 \cdot 3a =\]

\[= a^{2} + 6a + 9 - 12a =\]

\[= a^{2} - 6a + 9 = (a - 3)^{2}\]

\[1)\ \ D = 0;\ a = 3:\]

\[x = \frac{3 + 3 \pm |3 - 3|}{2} = \frac{6}{2} = 3.\]

\[2)\ \ D > 0;a > 3:\]

\[x_{1} = \frac{a + 3 + a - 3}{2} = \frac{2a}{2} = a;\]

\[x_{2} = \frac{a + 3 - a + 3}{2} = \frac{6}{2} = 3.\]

\[Ответ:a = 3 \Longrightarrow x = 3;\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ a > 3 \Longrightarrow x_{1} = a;\ \ x_{2} = 3.\]