\frac{4 m + ρ_{v} (1 - β) 8 V}{8 V} = ρ_{v} \Rightarrow \frac{m}{2 V} = β ρ_{v}

${\frac{4m + \rho_v(1 - \beta)8V}{8V} = \rho_v \quad\Rightarrow\quad \frac{m}{2V} = \beta\rho_v}$

Error