2025 RVHS Promo Q3

A curve \(C\) has equation \(y=ax-b+\frac{b}{x+1}\), where \(a\) and \(b\) are real constants such that \(a>0\), \(b<0\) and \(x\ne -1\).

1. Use differentiation to show that \(C\) does not have any stationary points.[3]

It is now given that \(b=-a\).

3. Sketch \(C\), giving the equations of the asymptotes and the coordinates of the points where \(C\) crosses the axes.[3]