Solve (1-sqrt{3})=(1+sqrt{3})(x-1)

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

Solve for x

$$x=\sqrt{3}-1\approx 0.732050808$$

Steps for Solving Linear Equation

Apply the distributive property by multiplying each term of 1+\sqrt{3} by each term of x-1.

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

Swap sides so that all variable terms are on the left hand side.

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

Add 1 to both sides.

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

Add 1 and 1 to get 2.

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

Add \sqrt{3} to both sides.

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

Combine -\sqrt{3} and \sqrt{3} to get 0.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+\sqrt{3}.

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

Dividing by 1+\sqrt{3} undoes the multiplication by 1+\sqrt{3}.

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

Divide 2 by 1+\sqrt{3}.

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