Solve y=x-1/x+1

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

Solve for x

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

$$y\neq 1$$

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.

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

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

$$yx+y=x-1$$

Subtract x from both sides.

$$yx+y-x=-1$$

Subtract y from both sides.

$$yx-x=-1-y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-1.

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

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

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

Divide -1-y by y-1.

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

Variable x cannot be equal to -1.

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

Solve for y

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

$$x\neq -1$$