Solve x/sqrt{2}-sqrt{2}=

$$\frac { x } { \sqrt { 2 } } - \sqrt { 2 } =$$

Evaluate

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

Short Solution Steps

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

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

The square of \sqrt{2} is 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2} times \frac{2}{2}.

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

Since \frac{x\sqrt{2}}{2} and \frac{2\sqrt{2}}{2} have the same denominator, subtract them by subtracting their numerators.

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

Factor

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

Solution Steps

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

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

The square of \sqrt{2} is 2.

$$factor(\frac{x\sqrt{2}}{2}-\sqrt{2})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2} times \frac{2}{2}.

$$factor(\frac{x\sqrt{2}}{2}-\frac{2\sqrt{2}}{2})$$

Since \frac{x\sqrt{2}}{2} and \frac{2\sqrt{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{x\sqrt{2}-2\sqrt{2}}{2})$$

Consider x\sqrt{2}-2\sqrt{2}. Factor out \sqrt{2}.

$$\sqrt{2}\left(x-2\right)$$

Rewrite the complete factored expression.

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