7 A curve has equation \(y = \frac { ( x + 1 ) ( 2 x - 1 ) } { x ^ { 2 } - 3 }\).
- Find the coordinates of the points where the curve crosses the axes.
- Write down the equations of the three asymptotes.
- Determine whether the curve approaches the horizontal asymptote from above or from below for
(A) large positive values of \(x\),
(B) large negative values of \(x\). - Sketch the curve.
- Solve the inequality \(\frac { ( x + 1 ) ( 2 x - 1 ) } { x ^ { 2 } - 3 } < 2\).