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

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

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

\[= a^{2} + 6a + 9 - 8a - 8 =\]

\[= a^{2} - 2a + 1 = (a - 1)^{2}\]

\[x_{1,2} = \frac{a + 3 \pm \sqrt{(a - 1)^{2}}}{2} =\]

\[= \frac{a + 3 \pm |a - 1|}{2}\]

\[1.\ При\ D = 0:\ \ \]

\[(a - 1)^{2} = 0\]

\[a - 1 = 0\ \ \]

\[a = 1.\]

\[x = \frac{1 + 3 \pm 0}{2} =\]

\[= \frac{4}{2} = 2 - не\ подходит.\]

\[2.\ При\ \ a \neq 1:\]

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

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

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

\[= \frac{4}{2} = 2 - не\ подходит.\]