9 A curve which passes through \(( 0,3 )\) has equation \(y = \mathrm { f } ( x )\). It is given that \(\mathrm { f } ^ { \prime } ( x ) = 1 - \frac { 2 } { ( x - 1 ) ^ { 3 } }\).
- Find the equation of the curve.
The tangent to the curve at \(( 0,3 )\) intersects the curve again at one other point, \(P\). - Show that the \(x\)-coordinate of \(P\) satisfies the equation \(( 2 x + 1 ) ( x - 1 ) ^ { 2 } - 1 = 0\).
- Verify that \(x = \frac { 3 } { 2 }\) satisfies this equation and hence find the \(y\)-coordinate of \(P\).