Solve xy=x+y

$$xy=x+y$$

Solve for x

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

$$y\neq 1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xy-x=y$$

Combine all terms containing x.

$$\left(y-1\right)x=y$$

Divide both sides by y-1.

$$\frac{\left(y-1\right)x}{y-1}=\frac{y}{y-1}$$

Dividing by y-1 undoes the multiplication by y-1.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$xy-y=x$$

Combine all terms containing y.

$$\left(x-1\right)y=x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)y}{x-1}=\frac{x}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

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