Solve (4/3-sqrt{3})divsqrt{3}

$$( \frac{ 4 }{ 3 } - \sqrt{ 3 } ) \div \sqrt{ 3 }$$

Evaluate

$$\frac{4\sqrt{3}}{9}-1\approx -0.230199641$$

Solution Steps

Rationalize the denominator of \frac{\frac{4}{3}-\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(\frac{4}{3}-\sqrt{3}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(\frac{4}{3}-\sqrt{3}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply \frac{4}{3}-\sqrt{3} by \sqrt{3}.

$$\frac{\frac{4}{3}\sqrt{3}-\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{4}{3}\sqrt{3}-3}{3}$$

Factor

$$\frac{4 \sqrt{3} - 9}{9} = -0.23019964108049903$$