Solve frac{sqrt{2}}{4}x-1/sqrt{2}y

$$\frac{ \sqrt{ 2 } }{ 4 } x- \frac{ 1 }{ \sqrt{ 2 } } y$$

Factor

$$\frac{\sqrt{2}\left(x-2y\right)}{4}$$

Solution Steps

Express \frac{\sqrt{2}}{4}x as a single fraction.

$$factor(\frac{\sqrt{2}x}{4}-\frac{1}{\sqrt{2}}y)$$

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

$$factor(\frac{\sqrt{2}x}{4}-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}y)$$

The square of \sqrt{2} is 2.

$$factor(\frac{\sqrt{2}x}{4}-\frac{\sqrt{2}}{2}y)$$

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

$$factor(\frac{\sqrt{2}x}{4}-\frac{\sqrt{2}y}{2})$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{\sqrt{2}y}{2} times \frac{2}{2}.

$$factor(\frac{\sqrt{2}x}{4}-\frac{2\sqrt{2}y}{4})$$

Since \frac{\sqrt{2}x}{4} and \frac{2\sqrt{2}y}{4} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{\sqrt{2}x-2\sqrt{2}y}{4})$$

Do the multiplications in \sqrt{2}x-2\sqrt{2}y.

$$factor(\frac{\sqrt{2}x-2y\sqrt{2}}{4})$$

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

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

Rewrite the complete factored expression.

$$\frac{\left(x-2y\right)\sqrt{2}}{4}$$

Evaluate

$$\frac{\sqrt{2}\left(x-2y\right)}{4}$$