3.2: Quotient rule and unique stationary point

Show that $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ can be written in the form $\dfrac{(2x^{2} + 10)^{\frac{1}{2}}}{(x - 1)^{2}}\left(Ax^{2} + Bx + C\right)$, where $A$, $B$ and $C$ are integers.

Show that, for $x > 1$, the curve has exactly one stationary point. Find the value of $x$ at this stationary point.