Solve 1/x-1/y=1

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

Solve for y

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

$$x\neq 0\text{ and }x\neq 1$$

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 x,y.

$$y-x=xy$$

Subtract xy from both sides.

$$y-x-xy=0$$

Add x to both sides. Anything plus zero gives itself.

$$y-xy=x$$

Combine all terms containing y.

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

Divide both sides by 1-x.

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

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

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

Variable y cannot be equal to 0.

$$y=\frac{x}{1-x}\text{, }y\neq 0$$

Solve for x

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

$$y\neq 0\text{ and }y\neq -1$$