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

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

Solve for x

$$x = \frac{3 \sqrt{2}}{4} \approx 1.060660172$$

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.

$$\frac{2}{3}x\times 3^{\frac{1}{2}}\times 2\sqrt{2}=2\sqrt{3}$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{2\times 2}{3}x\times 3^{\frac{1}{2}}\sqrt{2}=2\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}x\times 3^{\frac{1}{2}}\sqrt{2}=2\sqrt{3}$$

Reorder the terms.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{4}{3}\sqrt{6}x=2\sqrt{3}$$

The equation is in standard form.

$$\frac{4\sqrt{6}}{3}x=2\sqrt{3}$$

Divide both sides by \frac{4}{3}\sqrt{6}.

$$\frac{3\times \frac{4\sqrt{6}}{3}x}{4\sqrt{6}}=\frac{3\times 2\sqrt{3}}{4\sqrt{6}}$$

Dividing by \frac{4}{3}\sqrt{6} undoes the multiplication by \frac{4}{3}\sqrt{6}.

$$x=\frac{3\times 2\sqrt{3}}{4\sqrt{6}}$$

Divide 2\sqrt{3} by \frac{4}{3}\sqrt{6}.

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