Find the quotient and the remainder when \(x ^ { 2 } - 5 x + 6\) is divided by \(x - 1\).
(a) Find the general solution of the differential equation
$$\left( \frac { x - 1 } { x ^ { 2 } - 5 x + 6 } \right) \frac { \mathrm { d } y } { \mathrm {~d} x } = y - 5 .$$
(b) Given that \(y = 7\) when \(x = 8\), find \(y\) when \(x = 6\).