Let's first simplify the expressions under the square roots:
8 + 2√12 = 8 + 2 2√3 = 8 + 4√3 = 4(2 + √38 - 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).
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).