Solve x-1/x+1=sqrt{2}

$$\frac { x - 1 } { x + 1 } = \sqrt { 2 }$$

Solve for x

$$x=-2\sqrt{2}-3\approx -5.828427125$$

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.

$$x-1=\left(x+1\right)\sqrt{2}$$

Use the distributive property to multiply x+1 by \sqrt{2}.

$$x-1=x\sqrt{2}+\sqrt{2}$$

Subtract x\sqrt{2} from both sides.

$$x-1-x\sqrt{2}=\sqrt{2}$$

Add 1 to both sides.

$$x-x\sqrt{2}=\sqrt{2}+1$$

Combine all terms containing x.

$$\left(1-\sqrt{2}\right)x=\sqrt{2}+1$$

Divide both sides by 1-\sqrt{2}.

$$\frac{\left(1-\sqrt{2}\right)x}{1-\sqrt{2}}=\frac{\sqrt{2}+1}{1-\sqrt{2}}$$

Dividing by 1-\sqrt{2} undoes the multiplication by 1-\sqrt{2}.

$$x=\frac{\sqrt{2}+1}{1-\sqrt{2}}$$

Divide \sqrt{2}+1 by 1-\sqrt{2}.

$$x=-2\sqrt{2}-3$$