Solve xdivy=zdivx

$$x \div y=z \div x$$

Solve for y

$$y=\frac{x^{2}}{z}$$

$$x\neq 0\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of y,x.

$$xx=yz$$

Multiply x and x to get x^{2}.

$$x^{2}=yz$$

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

$$yz=x^{2}$$

The equation is in standard form.

$$zy=x^{2}$$

Divide both sides by z.

$$\frac{zy}{z}=\frac{x^{2}}{z}$$

Dividing by z undoes the multiplication by z.

$$y=\frac{x^{2}}{z}$$

Variable y cannot be equal to 0.

$$y=\frac{x^{2}}{z}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=-\sqrt{y}\sqrt{z}$$

$$x=\sqrt{y}\sqrt{z}\text{, }y\neq 0\text{ and }z\neq 0$$

Solve for x

$$x=\sqrt{yz}$$

$$x=-\sqrt{yz}\text{, }\left(z<0\text{ and }y<0\right)\text{ or }\left(y>0\text{ and }z>0\right)$$