Solve x-y=z/ydivz

$$x-y= \frac{ z }{ y } \div z$$

Solve for x

$$x=y+\frac{1}{y}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by z.

$$zx-yz=\frac{z}{y}$$

Add yz to both sides.

$$zx=\frac{z}{y}+yz$$

To add or subtract expressions, expand them to make their denominators the same. Multiply yz times \frac{y}{y}.

$$zx=\frac{z}{y}+\frac{yzy}{y}$$

Since \frac{z}{y} and \frac{yzy}{y} have the same denominator, add them by adding their numerators.

$$zx=\frac{z+yzy}{y}$$

Do the multiplications in z+yzy.

$$zx=\frac{z+y^{2}z}{y}$$

Multiply both sides of the equation by y.

$$zxy=z+y^{2}z$$

The equation is in standard form.

$$yzx=zy^{2}+z$$

Divide both sides by zy.

$$\frac{yzx}{yz}=\frac{zy^{2}+z}{yz}$$

Dividing by zy undoes the multiplication by zy.

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

Divide z+zy^{2} by zy.

$$x=y+\frac{1}{y}$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{x^{2}-4}+x}{2}$$

$$y=\frac{\sqrt{x^{2}-4}+x}{2}\text{, }z\neq 0$$

Solve for y

$$y=\frac{-\sqrt{x^{2}-4}+x}{2}$$

$$y=\frac{\sqrt{x^{2}-4}+x}{2}\text{, }z\neq 0\text{ and }|x|\geq 2$$