Here's the way lynx got the second answer
√2 - √6
______ multiply top/bottom by the conjugate of the denominator ⇒ √2 - √6
√2 + √6
√2 -√6 √2 - √6 2 - 2√12 + 6 8 - 2*2√3
______ _____ = ___________ = __________ =
√2 + √6 √2 - √6 2 - 6 -4
8/-4 + -4√3 / - 4
-2 + √3