Solve =frac{1/sqrt{2}*sqrt{3}}{-1/sqrt{3}}

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

Evaluate

$$-\frac{3\sqrt{2}}{2}\approx -2.121320344$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{3}}{\frac{-1}{\sqrt{3}}}$$

The square of \sqrt{2} is 2.

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

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

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

Rationalize the denominator of \frac{-1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

$$\frac{\sqrt{2}\sqrt{3}\times 3}{2\left(-1\right)\sqrt{3}}$$

Cancel out \sqrt{3} in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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