Express \(\frac { 1 } { ( 3 - x ) ( 6 - x ) }\) in partial fractions.
In a chemical reaction, the amount \(x\) grams of a substance at time \(t\) seconds is related to the rate at which \(x\) is changing by the equation
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = k ( 3 - x ) ( 6 - x )$$
where \(k\) is a constant. When \(t = 0 , x = 0\) and when \(t = 1 , x = 1\).
(a) Show that \(k = \frac { 1 } { 3 } \ln \frac { 5 } { 4 }\).
(b) Find the value of \(x\) when \(t = 2\).