Solve 1/2/-sqrt{3/2}

$$\frac{ \frac{ 1 }{ 2 } }{ \frac{ - \sqrt{ 3 } }{ 2 } }$$

Evaluate

$$-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Solution Steps

Divide \frac{1}{2} by \frac{-\sqrt{3}}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{-\sqrt{3}}{2}.

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

Multiply 2 and -1 to get -2.

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

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

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

The square of \sqrt{3} is 3.

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

Cancel out 2 in both numerator and denominator.

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