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

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

Solve for x

$$x=-\left(\sqrt{3}+1\right)\approx -2.732050808$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

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

Subtract x\times 2 from both sides.

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

Combine x and -x\times 2 to get -x.

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

Add \sqrt{3}x to both sides.

$$-x+2+\sqrt{3}x=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

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}.

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