P$6\mathrm{.}14$ For the separator flow sheet with recycle $($Fig$.6\mathrm{.}7),$ the overall recovery of component $B,f_{RB},$ is related to the recovery of component $B$ in the separator unit, $f_{RB1},$ and the fractional split $f_S,$ as $f_{RB}=f_{RB1}/(1-f_S(1-f_{RB1})).$ Derive the relationship between $f_{RB}$ and $f_{RB1}$ for two cases: $f_S=0$ and $f_S=1.$ Explain briefly why your result makes sense in each case.