2ab/a^2-6ab+9b^2*(a^2-9b^2)

To simplify the given expression \(2ab/(a^2 - 6ab + 9b^2) \times (a^2 - 9b^2)\), follow these steps:

Step 1: Factor the denominator of the first fraction: \(a^2 - 6ab + 9b^2\) can be factored into \((a - 3b)^2\).

Step 2: Simplify the expression: \(2ab/(a^2 - 6ab + 9b^2) \times (a^2 - 9b^2) = 2ab/(a - 3b)^2 \times (a + 3b)(a - 3b)\).

Step 3: Cancel out common factors: The term \((a - 3b)\) in the numerator and denominator will cancel out, leaving you with \(2ab \times (a + 3b) = 2ab(a + 3b)\).

So, the simplified form of the given expression is \(2ab(a + 3b)\).