Answer
See explanation
Work Step by Step
The definition for volume expansivity is $$
\beta=\frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
$$ According to the cyclic relation, $$
\left(\frac{\partial v}{\partial T}\right)_P\left(\frac{\partial P}{\partial v}\right)_T\left(\frac{\partial T}{\partial P}\right)_v=-1
$$ which on rearrangement becomes $$
\left(\frac{\partial v}{\partial T}\right)_P=-\frac{\left(\frac{\partial P}{\partial T}\right)_v}{\left(\frac{\partial P}{\partial v}\right)_T}
$$ Proceeding to perform the differentiations gives $$
\left(\frac{\partial P}{\partial T}\right)_v=\frac{R}{v-b}+\frac{a}{v^2 T^2}
$$ and $$
\left(\frac{\partial P}{\partial v}\right)_T=-\frac{R T}{(v-b)^2}+\frac{2 a}{v^3 T}
$$ Substituting these results into the definition of the volume expansivity produces $$
\beta=-\frac{1}{v} \frac{\frac{R}{v-b}+\frac{a}{v^2 T^2}}{\frac{-R T}{(v-b)^2}+\frac{2 a}{v^3 T}}
$$
