The curve \(C\) has equation
\(y=\frac{x^{2}-2 x+\lambda}{x+1},\)
where \(\lambda\) is a constant. Show that the equations of the asymptotes of \(C\) are independent of \(\lambda\).

Find the value of \(\lambda\) for which the \(x\)-axis is a tangent to \(C\), and sketch \(C\) in this case.

Sketch \(C\) in the case \(\lambda=-4\), giving the exact coordinates of the points of intersection of \(C\) with the \(x\)-axis.