The Chain Rule & Implicit Differentiation · Challenge problem

A gas obeys the (dimensionless) van der Waals equation $\left(P + \dfrac{2}{V^2}\right)(V - 1) = T$. At the state with $V = 2$ and $T = 3$, find the thermal expansion rate $\left(\dfrac{\partial V}{\partial T}\right)_P$, the rate of change of $V$ with $T$ when the pressure is held constant.