A curve with equation \(\displaystyle y=ax+b+\frac{c}{x-1}\), where \(a\), \(b\) and \(c\) are non-zero constants, has a turning point at \((3,7)\). Given that the area bounded by the curve for \(y>0\), the \(x\)-axis, the lines \(x=2\) and \(x=3\) is \(4.5+\ln16\text{ units}^2\), find the values of \(a\), \(b\) and \(c\).[5]
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