Let's first simplify the expressions under the square roots:

8 + 2√12 = 8 + 2 2√3 = 8 + 4√3 = 4(2 + √3)
8 - 2√12 = 8 - 2 2√3 = 8 - 4√3 = 4(2 - √3)

Now, let's substitute these values back into the given expression and simplify it further:

(SQR(4(2 + √3)) - √2) / (SQR(4(2 - √3)) + √2)
= (√(4) √(2 + √3) - √2) / (√(4) √(2 - √3) + √2)
= (2√(2 + √3) - √2) / (2√(2 - √3) + √2)
= (2√2 + 2√3 - √2) / (2√2 - 2√3 + √2)
= (√2 + 2√3) / (√2 - 2√3)

Therefore, the simplified form of the given expression is (√2 + 2√3) / (√2 - 2√3).