Solve xy=x/y

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=1\text{ or }y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$xyy=x$$

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

$$xy^{2}=x$$

Subtract x from both sides.

$$xy^{2}-x=0$$

Combine all terms containing x.

$$\left(y^{2}-1\right)x=0$$

Divide 0 by y^{2}-1.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&|y|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$xyy=x$$

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

$$xy^{2}=x$$

Subtract x from both sides.

$$xy^{2}-x=0$$

Combine all terms containing x.

$$\left(y^{2}-1\right)x=0$$

Divide 0 by y^{2}-1.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=1\text{; }y=-1\text{, }&\text{unconditionally}\\y\neq 0\text{, }&x=0\end{matrix}\right.$$