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

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

Solve for x

$$x=\frac{9-4\sqrt{2}}{7}\approx 0.47759225$$

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.

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

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

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

Add 2x\sqrt{2} to both sides.

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

Subtract 1 from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

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

$$x=\frac{9-4\sqrt{2}}{7}$$