Solve frac{x_{1}}{x_{2}}=x_{3}

$$\frac { x _ { 1 } } { x _ { 2 } } = x _ { 3 }$$

Solve for x_2

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

Steps for Solving Linear Equation

Variable x_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x_{2}.

$$x_{1}=x_{3}x_{2}$$

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

$$x_{3}x_{2}=x_{1}$$

Divide both sides by x_{3}.

$$\frac{x_{3}x_{2}}{x_{3}}=\frac{x_{1}}{x_{3}}$$

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

$$x_{2}=\frac{x_{1}}{x_{3}}$$

Variable x_{2} cannot be equal to 0.

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

Solve for x_1

$$x_{1}=x_{2}x_{3}$$

$$x_{2}\neq 0$$

Solution Steps

Multiply both sides of the equation by x_{2}.

$$x_{1}=x_{3}x_{2}$$