Solve frac{sqrt{7}}{frac{sqrt{3}}{2}}=3/x

$$\frac { \sqrt { 7 } } { \frac { \sqrt { 3 } } { 2 } } = \frac { 3 } { x }$$

Solve for x

$$x=\frac{3\sqrt{21}}{14}\approx 0.981980506$$

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.

$$\frac{2}{3}x\times 3^{\frac{1}{2}}\sqrt{7}=3$$

Reorder the terms.

$$\frac{2}{3}\sqrt{3}\sqrt{7}x=3$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{2}{3}\sqrt{21}x=3$$

The equation is in standard form.

$$\frac{2\sqrt{21}}{3}x=3$$

Divide both sides by \frac{2}{3}\sqrt{21}.

$$\frac{3\times \frac{2\sqrt{21}}{3}x}{2\sqrt{21}}=\frac{3\times 3}{2\sqrt{21}}$$

Dividing by \frac{2}{3}\sqrt{21} undoes the multiplication by \frac{2}{3}\sqrt{21}.

$$x=\frac{3\times 3}{2\sqrt{21}}$$

Divide 3 by \frac{2}{3}\sqrt{21}.

$$x=\frac{3\sqrt{21}}{14}$$