Solve x=-frac{2sqrt{3}}{1-sqrt{3}}

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

Solve for x

$$x=\sqrt{3}+3\approx 4.732050808$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{2\sqrt{3}}{1-\sqrt{3}} by multiplying numerator and denominator by 1+\sqrt{3}.

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

Consider \left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square 1. Square \sqrt{3}.

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

Subtract 3 from 1 to get -2.

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

Cancel out -2 and -2.

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

Use the distributive property to multiply -\sqrt{3} by 1+\sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To find the opposite of -\sqrt{3}-3, find the opposite of each term.

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

The opposite of -\sqrt{3} is \sqrt{3}.

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

The opposite of -3 is 3.

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

Assign x

$$x≔\sqrt{3}+3$$