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

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

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

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.

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

Reorder the terms.

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

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

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

Divide both sides by \sqrt{6}.

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

Dividing by \sqrt{6} undoes the multiplication by \sqrt{6}.

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

Divide \sqrt{3} by \sqrt{6}.

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