Solve R_{v}=(n-1)*R_{m}

$$R _ { v } = ( n - 1 ) \cdot R _ { m }$$

Solve for R_m

$$\left\{\begin{matrix}R_{m}=-\frac{R_{v}}{1-n}\text{, }&n\neq 1\\R_{m}\in \mathrm{R}\text{, }&R_{v}=0\text{ and }n=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by R_{m}.

$$R_{v}=nR_{m}-R_{m}$$

Swap sides so that all variable terms are on the left hand side.

$$nR_{m}-R_{m}=R_{v}$$

Combine all terms containing R_{m}.

$$\left(n-1\right)R_{m}=R_{v}$$

Divide both sides by n-1.

$$\frac{\left(n-1\right)R_{m}}{n-1}=\frac{R_{v}}{n-1}$$

Dividing by n-1 undoes the multiplication by n-1.

$$R_{m}=\frac{R_{v}}{n-1}$$

Solve for R_v

$$R_{v}=R_{m}\left(n-1\right)$$

Solution Steps

Use the distributive property to multiply n-1 by R_{m}.

$$R_{v}=nR_{m}-R_{m}$$