Express \(\frac { \left( x ^ { 2 } - 8 x + 9 \right) } { ( x + 1 ) ( x - 2 ) ^ { 2 } }\) in partial fractions.
Express \(y\) in terms of \(x\) given that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y \left( x ^ { 2 } - 8 x + 9 \right) } { ( x + 1 ) ( x - 2 ) ^ { 2 } } \text { and } y = 16 \text { when } x = 3 .$$
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