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

Add y to 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.

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