5 The curve \(C\) has equation \(y = \frac { x } { ( x + 1 ) ( x - 2 ) }\).
The line \(L\) has equation \(y = - \frac { 1 } { 2 }\).
- Write down the equations of the asymptotes of \(C\).
- The line \(L\) intersects the curve \(C\) at two points. Find the \(x\)-coordinates of these two points.
- Sketch \(C\) and \(L\) on the same axes.
(You are given that the curve \(C\) has no stationary points.) - Solve the inequality
$$\frac { x } { ( x + 1 ) ( x - 2 ) } \leqslant - \frac { 1 } { 2 }$$