Solve (x-xsqrt{2})divsqrt{2}

$$(x-x \sqrt{ 2 } ) \div \sqrt{ 2 }$$

Factor

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

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Use the distributive property to multiply x-x\sqrt{2} by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply -1 and 2 to get -2.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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