Solve y=1/x-1

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

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

Use the distributive property to multiply y by x-1.

$$yx-y=1$$

Add y to both sides.

$$yx=1+y$$

The equation is in standard form.

$$yx=y+1$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Divide y+1 by y.

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

Variable x cannot be equal to 1.

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

Solve for y

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

$$x\neq 1$$