Solve [frac{R_{1}}{R_{2}}=frac{R_{3}}{R_{4}}]

$$[ \frac { R _ { 1 } } { R _ { 2 } } = \frac { R _ { 3 } } { R _ { 4 } } ]$$

Solve for R_1

$$R_{1}=\frac{R_{2}R_{3}}{R_{4}}$$

$$R_{2}\neq 0\text{ and }R_{4}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{2}R_{4}, the least common multiple of R_{2},R_{4}.

$$R_{4}R_{1}=R_{2}R_{3}$$

Divide both sides by R_{4}.

$$\frac{R_{4}R_{1}}{R_{4}}=\frac{R_{2}R_{3}}{R_{4}}$$

Dividing by R_{4} undoes the multiplication by R_{4}.

$$R_{1}=\frac{R_{2}R_{3}}{R_{4}}$$

Solve for R_2

$$\left\{\begin{matrix}R_{2}=\frac{R_{1}R_{4}}{R_{3}}\text{, }&R_{4}\neq 0\text{ and }R_{1}\neq 0\text{ and }R_{3}\neq 0\\R_{2}\neq 0\text{, }&R_{3}=0\text{ and }R_{1}=0\text{ and }R_{4}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable R_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R_{2}R_{4}, the least common multiple of R_{2},R_{4}.

$$R_{4}R_{1}=R_{2}R_{3}$$

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

$$R_{2}R_{3}=R_{4}R_{1}$$

The equation is in standard form.

$$R_{3}R_{2}=R_{1}R_{4}$$

Divide both sides by R_{3}.

$$\frac{R_{3}R_{2}}{R_{3}}=\frac{R_{1}R_{4}}{R_{3}}$$

Dividing by R_{3} undoes the multiplication by R_{3}.

$$R_{2}=\frac{R_{1}R_{4}}{R_{3}}$$

Variable R_{2} cannot be equal to 0.

$$R_{2}=\frac{R_{1}R_{4}}{R_{3}}\text{, }R_{2}\neq 0$$