A curve has equation

\(y=\frac{(2x^2+10)^{\frac32}}{x-1}\quad\text{for }x\gt 1.\)

(a) Show that \(\dfrac{dy}{dx}\) can be written in the form

\(\frac{(2x^2+10)^{\frac12}}{(x-1)^2}(Ax^2+Bx+C),\)

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

(b) Show that, for \(x\gt 1\), the curve has exactly one stationary point. Find the value of \(x\) at this stationary point.