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

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

Solve for x

$$x=2$$

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 2x, the least common multiple of 2,x.

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

Use the distributive property to multiply 2 by x-2+\sqrt{3}.

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

Subtract 2x from both sides.

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

Combine all terms containing x.

$$\left(\sqrt{3}-2\right)x=-4+2\sqrt{3}$$

The equation is in standard form.

$$\left(\sqrt{3}-2\right)x=2\sqrt{3}-4$$

Divide both sides by -2+\sqrt{3}.

$$\frac{\left(\sqrt{3}-2\right)x}{\sqrt{3}-2}=\frac{2\sqrt{3}-4}{\sqrt{3}-2}$$

Dividing by -2+\sqrt{3} undoes the multiplication by -2+\sqrt{3}.

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

Divide -4+2\sqrt{3} by -2+\sqrt{3}.

$$x=2$$