Solve 2x-2/sqrt{2}

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

Evaluate

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

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

Divide each term of 2x\sqrt{2}-2\sqrt{2} by 2 to get -\sqrt{2}+\sqrt{2}x.

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

Factor

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

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

Divide each term of 2x\sqrt{2}-2\sqrt{2} by 2 to get -\sqrt{2}+\sqrt{2}x.

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

Factor out \sqrt{2}.

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