Solve frac{3sqrt{10}}{frac{sqrt{2}}{2}}=frac{3sqrt{2}}{x}

$$\frac { 3 \sqrt { 10 } } { \frac { \sqrt { 2 } } { 2 } } = \frac { 3 \sqrt { 2 } } { x }$$

Solve for x

$$x=\frac{\sqrt{10}}{10}\approx 0.316227766$$

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.

$$x\times 2^{\frac{1}{2}}\times 3\sqrt{10}=3\sqrt{2}$$

Reorder the terms.

$$3\sqrt{2}\sqrt{10}x=3\sqrt{2}$$

Cancel out 3 on both sides.

$$\sqrt{2}\sqrt{10}x=\sqrt{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\sqrt{2}\sqrt{2}\sqrt{5}x=\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{5}x=\sqrt{2}$$

Divide both sides by 2\sqrt{5}.

$$\frac{2\sqrt{5}x}{2\sqrt{5}}=\frac{\sqrt{2}}{2\sqrt{5}}$$

Dividing by 2\sqrt{5} undoes the multiplication by 2\sqrt{5}.

$$x=\frac{\sqrt{2}}{2\sqrt{5}}$$

Divide \sqrt{2} by 2\sqrt{5}.

$$x=\frac{\sqrt{10}}{10}$$