To simplify the expression 3a + 6b / 3 (a - 2b)^2 / 4b^2 - a^2, we first need to apply the order of operations (PEMDAS/BODMAS):

Perform the operations inside the parentheses: (a - 2b)^2 = a^2 - 4ab + 4b^2Multiply the expression by 3: 3(a^2 - 4ab + 4b^2) = 3a^2 - 12ab + 12b^2Divide 6b by 3: 6b / 3 = 2bSubstitute the values back into the expression: 3a + 2b / (3a^2 - 12ab + 12b^2) / 4b^2 - a^2Evaluate the denominator: 4b^2 - a^2 = (2b + a)(2b - a)Now the expression becomes: 3a + 2b / (3a^2 - 12ab + 12b^2) / (2b + a)(2b - a)Perform the division: (3a + 2b) / (3a^2 - 12ab + 12b^2) * (2b + a)(2b - a)The simplified expression is (3a + 2b) / (3a - 6b)^2(2b + a)