Which of the following is equal to (2)/(sqrt (6)-sqrt (2)) A (sqrt (6)+sqrt (2))/(2) B. (1)/(2) C. (sqrt (6)+sqrt (2))/(4) D. (sqrt (6)-sqrt (2))/(2) E. (1)/(sqrt (3)-sqrt (1)) F. (sqrt (6)-sqrt (2))/(4)

## Step 1: Rationalizing the Denominator<br />### To simplify the expression, we multiply the numerator and denominator by the conjugate of the denominator, which is $\sqrt{6} + \sqrt{2}$.<br /><br />## Step 2: Multiplication<br />### Multiply the numerator and denominator by the conjugate:<br />$ \frac{2}{\sqrt{6} - \sqrt{2}} \cdot \frac{\sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}} = \frac{2(\sqrt{6} + \sqrt{2})}{(\sqrt{6} - \sqrt{2})(\sqrt{6} + \sqrt{2})} $<br /><br />## Step 3: Simplification<br />### Simplify the expression:<br />$ \frac{2(\sqrt{6} + \sqrt{2})}{6 - 2} = \frac{2(\sqrt{6} + \sqrt{2})}{4} = \frac{\sqrt{6} + \sqrt{2}}{2} $