1/✓6-2 - 1/✓6+2

To simplify the expression \( \frac{1}{\sqrt{6} - 2} - \frac{1}{\sqrt{6} + 2} \), we can find a common denominator and combine the two fractions.

The denominators are \( \sqrt{6} - 2 \) and \( \sqrt{6} + 2 \). The common denominator is \( (\sqrt{6} - 2)(\sqrt{6} + 2) \).

Now we can rewrite the expression:

\[ \frac{1}{\sqrt{6} - 2} - \frac{1}{\sqrt{6} + 2} = \frac{(\sqrt{6} + 2) - (\sqrt{6} - 2)}{(\sqrt{6} - 2)(\sqrt{6} + 2)} \]

Now let's simplify the numerator:

\[ (\sqrt{6} + 2) - (\sqrt{6} - 2) = \sqrt{6} + 2 - \sqrt{6} + 2 = 4 \]

So, the expression now looks like:

\[ \frac{4}{(\sqrt{6} - 2)(\sqrt{6} + 2)} \]

Next, we can simplify the denominator. Notice that:

\[ (\sqrt{6} - 2)(\sqrt{6} + 2) = \sqrt{6}^2 - 2^2 = 6 - 4 = 2 \]

Putting this all together, we have:

\[ \frac{4}{2} = 2 \]

Thus, the simplified result of the original expression is:

\[ \boxed{2} \]