Solve 10/3/frac{2{3}sqrt{5}}=frac{sqrt{5}}{x}

$$\frac { \frac { 10 } { 3 } } { \frac { 2 } { 3 } \sqrt { 5 } } = \frac { \sqrt { 5 } } { x }$$

Solve for x

$$x=1$$

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.

$$\frac{3}{10}x\times 5^{\frac{1}{2}}\times \frac{10}{3}=\sqrt{5}$$

Cancel out \frac{3}{10} and its reciprocal \frac{10}{3}.

$$x\times 5^{\frac{1}{2}}=\sqrt{5}$$

Reorder the terms.

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

Divide both sides by \sqrt{5}.

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

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

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

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

$$x=1$$