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

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

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

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.

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

Reorder the terms.

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

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

$$\frac{1}{2}\sqrt{6}x=\sqrt{3}$$

The equation is in standard form.

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

Divide both sides by \frac{1}{2}\sqrt{6}.

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

Dividing by \frac{1}{2}\sqrt{6} undoes the multiplication by \frac{1}{2}\sqrt{6}.

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

Divide \sqrt{3} by \frac{1}{2}\sqrt{6}.

$$x=\sqrt{2}$$