An object has mass $m=\frac{p+1}{3p+1}$ and density $\rho = \frac{p^2-1}{9p^2+6p+1}$. Determine the volume $v$ where $\rho = \frac{m}{v}$. Also state the restrictions on any variables.

Question

$\begin{array}{1 1} (a)\; \frac{3p+1}{p-1} \\ (b)\; \frac{3p-1}{p+1} \\ (c)\; \frac{p+1}{3p-1} \\ (d)\; \frac{3p-1}{p-1} \end{array}$