Solve -frac{2/sqrt{3}}{sqrt{3}}

$$\frac { - \frac { 2 } { \sqrt { 3 } } } { \sqrt { 3 } }$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$\frac{-\frac{2\sqrt{3}}{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{-\frac{2\sqrt{3}}{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(-\frac{2\sqrt{3}}{3}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(-\frac{2\sqrt{3}}{3}\right)\sqrt{3}}{3}$$

Express \left(-\frac{2\sqrt{3}}{3}\right)\sqrt{3} as a single fraction.

$$\frac{\frac{-2\sqrt{3}\sqrt{3}}{3}}{3}$$

Express \frac{\frac{-2\sqrt{3}\sqrt{3}}{3}}{3} as a single fraction.

$$\frac{-2\sqrt{3}\sqrt{3}}{3\times 3}$$

Cancel out -1 in both numerator and denominator.

$$\frac{2\sqrt{3}\sqrt{3}}{-3\times 3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{2\times 3}{-3\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{-3\times 3}$$

Multiply -3 and 3 to get -9.

$$\frac{6}{-9}$$

Reduce the fraction \frac{6}{-9} to lowest terms by extracting and canceling out 3.

$$-\frac{2}{3}$$

Factor

$$-\frac{2}{3} = -0.6666666666666666$$