Solve x=frac{6sqrt{3}}{frac{sqrt{3}}{2}}

$$x = \frac { 6 \sqrt { 3 } } { \frac { \sqrt { 3 } } { 2 } }$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Divide 6\sqrt{3} by \frac{\sqrt{3}}{2} by multiplying 6\sqrt{3} by the reciprocal of \frac{\sqrt{3}}{2}.

$$x=\frac{6\sqrt{3}\times 2}{\sqrt{3}}$$

Multiply 6 and 2 to get 12.

$$x=\frac{12\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{12\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$x=\frac{12\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$x=\frac{12\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$x=\frac{12\times 3}{3}$$

Multiply 12 and 3 to get 36.

$$x=\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$x=12$$

Assign x

$$x≔12$$