Express \(\frac { x + 8 } { x ( x + 2 ) }\) in partial fractions.
By first using division, express \(\frac { 7 x ^ { 2 } + 16 x + 16 } { x ( x + 2 ) }\) in the form \(P + \frac { Q } { x } + \frac { R } { x + 2 }\).
A curve has parametric equations \(x = \frac { 2 t } { 1 - t } , y = 3 t + \frac { 4 } { t }\).
Show that the cartesian equation of the curve is \(y = \frac { 7 x ^ { 2 } + 16 x + 16 } { x ( x + 2 ) }\).
Find the area of the region bounded by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 2\). Give your answer in the form \(L + M \ln 2 + N \ln 3\).