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

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

Evaluate

$$1$$

Solution Steps

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

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

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{2}\left(-1\right)} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and -1 to get -2.

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

Divide 2 by -2 to get -1.

$$-\left(-1\right)$$

The opposite of -1 is 1.

$$1$$

Factor

$$1$$