SAT Mathematics Practice Test 2

Multiplying each side of $\mathit{R}=\frac{\mathit{F}}{\mathit{N}+\mathit{F}}$ by $\mathit{N}+\mathit{F}$ gives $\mathit{R}\left(\mathit{N}+\mathit{F}\right)=\mathit{F}$,which can b rewritten as $\mathit{R}\mathit{N}+\mathit{R}\mathit{F}=\mathit{F}$ Subtracting RF from each side of $\mathit{R}\mathit{N}+\mathit{R}\mathit{F}=\mathit{F}$ gives $\mathit{R}\mathit{N}=\mathit{F}-\mathit{R}\mathit{F}$, which can be factored as $\mathit{R}\mathit{N}=\mathit{F}\left(1-\mathit{R}\right)$.Finally,dividing each side of RN=F(1-R) by $1-\mathit{R}$ express F in terms of the other variable:$\mathit{F}=\frac{\mathit{R}\mathit{N}}{1-\mathit{R}}$
Subtracting $\mathit{R}\mathit{F}$ from each side of $\mathit{R}\mathit{N}+\mathit{R}\mathit{F}=\mathit{F}$ gives $\mathit{R}\mathit{N}=\mathit{F}-\mathit{R}\mathit{F}$, which can be factored