\frac{\sqrt{6 }+2 }{\sqrt{6}-2 }-\frac{\sqrt{6}-2 }{\sqrt{6}+2 }

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To simplify this expression, we'll first find a common denominator for the two fractions:

(\frac{\sqrt{6}+2}{\sqrt{6}-2} - \frac{\sqrt{6}-2}{\sqrt{6}+2})

Multiplying the denominators together, we get:

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

So, we rewrite the fractions with the common denominator of 2:

(\frac{(\sqrt{6}+2)^2 - (\sqrt{6}-2)^2}{(\sqrt{6}+2)(\sqrt{6}-2)})

Expanding the squares in the numerator, we get:

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

Simplify the numerator:

(\frac{8\sqrt{6}}{2})

Finally, simplify the expression:

(4\sqrt{6})