Solve x=y+1/y-1

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

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

$$xy-x=y+1$$

Subtract y from both sides.

$$xy-x-y=1$$

Add x to both sides.

$$xy-y=1+x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x-1.

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

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

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

Variable y cannot be equal to 1.

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

Solve for x

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

$$y\neq 1$$