Solve 1-x/1+x=3-2sqrt{2}

$$\frac { 1 - x } { 1 + x } = 3 - 2 \sqrt { 2 }$$

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

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.

$$1-x=\left(x+1\right)\times 3-2\sqrt{2}\left(x+1\right)$$

Use the distributive property to multiply x+1 by 3.

$$1-x=3x+3-2\sqrt{2}\left(x+1\right)$$

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

$$1-x=3x+3-2\sqrt{2}x-2\sqrt{2}$$

Subtract 3x from both sides.

$$1-x-3x=3-2\sqrt{2}x-2\sqrt{2}$$

Combine -x and -3x to get -4x.

$$1-4x=3-2\sqrt{2}x-2\sqrt{2}$$

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

$$1-4x+2\sqrt{2}x=3-2\sqrt{2}$$

Subtract 1 from both sides.

$$-4x+2\sqrt{2}x=3-2\sqrt{2}-1$$

Subtract 1 from 3 to get 2.

$$-4x+2\sqrt{2}x=2-2\sqrt{2}$$

Combine all terms containing x.

$$\left(-4+2\sqrt{2}\right)x=2-2\sqrt{2}$$

The equation is in standard form.

$$\left(2\sqrt{2}-4\right)x=2-2\sqrt{2}$$

Divide both sides by -4+2\sqrt{2}.

$$\frac{\left(2\sqrt{2}-4\right)x}{2\sqrt{2}-4}=\frac{2-2\sqrt{2}}{2\sqrt{2}-4}$$

Dividing by -4+2\sqrt{2} undoes the multiplication by -4+2\sqrt{2}.

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

Divide 2-2\sqrt{2} by -4+2\sqrt{2}.

$$x=\frac{\sqrt{2}}{2}$$