The curve \(C\) has equation
$$y = \frac { x ( x + 1 ) } { ( x - 1 ) ^ { 2 } }$$
- Obtain the equations of the asymptotes of \(C\).
- Show that there is exactly one point of intersection of \(C\) with the asymptotes and find its coordinates.
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and hence
(a) find the coordinates of any stationary points of \(C\),
(b) state the set of values of \(x\) for which the gradient of \(C\) is negative. - Draw a sketch of \(C\).