A curve has equation

\(y=\frac{(x^2-5)^{\frac13}}{x+1}\)

for \(x\gt -1\).

(a) Show that

\(\frac{dy}{dx}=\frac{Ax^2+Bx+C}{3(x+1)^2(x^2-5)^{\frac23}},\)

where \(A\), \(B\) and \(C\) are integers.

(b) Find the \(x\)-coordinate of the stationary point on the curve.

(c) Explain how you could determine the nature of this stationary point. You are not required to find the nature of this stationary point.