Solve a=frac{R_{1}L}{R}

$$a = \frac { R _ { 1 } L } { R }$$

Solve for L

$$\left\{\begin{matrix}L=\frac{Ra}{R_{1}}\text{, }&R_{1}\neq 0\text{ and }R\neq 0\\L\in \mathrm{R}\text{, }&a=0\text{ and }R_{1}=0\text{ and }R\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R.

$$aR=R_{1}L$$

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

$$R_{1}L=aR$$

The equation is in standard form.

$$R_{1}L=Ra$$

Divide both sides by R_{1}.

$$\frac{R_{1}L}{R_{1}}=\frac{Ra}{R_{1}}$$

Dividing by R_{1} undoes the multiplication by R_{1}.

$$L=\frac{Ra}{R_{1}}$$

Solve for R

$$\left\{\begin{matrix}R=\frac{LR_{1}}{a}\text{, }&L\neq 0\text{ and }R_{1}\neq 0\text{ and }a\neq 0\\R\neq 0\text{, }&\left(L=0\text{ or }R_{1}=0\right)\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R.

$$aR=R_{1}L$$

The equation is in standard form.

$$aR=LR_{1}$$

Divide both sides by a.

$$\frac{aR}{a}=\frac{LR_{1}}{a}$$

Dividing by a undoes the multiplication by a.

$$R=\frac{LR_{1}}{a}$$

Variable R cannot be equal to 0.

$$R=\frac{LR_{1}}{a}\text{, }R\neq 0$$