1.9: Product-rule differentiation and equation of a normal

Show that $\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{Px^{2} + Qx + 1}{(2x - 3)^{\frac{1}{2}}}$, where $P$ and $Q$ are integers.

Hence find the equation of the normal to the curve $y = (x^{2} + 1)(2x - 3)^{\frac{1}{2}}$ at the point where $x = 2$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.