(3((3x-1)/(x+3)) - 1) / (((3x-1)/(x+3)) + 3)

What would the answer be?
I already found the answer but I just want to check.

To evaluate the given expression (3((3x-1)/(x+3)) - 1) / (((3x-1)/(x+3)) + 3), we'll follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right). Let's simplify it step by step:

Step 1: Simplify the expressions inside the parentheses:
Inside the numerator:
3((3x-1)/(x+3)) - 1 = (9x - 3)/(x+3) - 1 = (9x - 3)/(x+3) - (x+3)/(x+3) = (9x - 3 - (x+3))/(x+3) = (9x - 3 - x - 3)/(x+3) = (8x - 6)/(x+3)

Inside the denominator:
((3x-1)/(x+3)) + 3 = (3x - 1)/(x+3) + 3 = (3x - 1)/(x+3) + 3(x+3)/(x+3) = (3x - 1 + 3(x+3))/(x+3) = (3x - 1 + 3x + 9) / (x+3) = (6x + 8)/(x+3)

Step 2: Substitute the simplified expressions back into the main expression:
(8x - 6)/(x+3) / (6x + 8)/(x+3)

Step 3: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator:
(8x - 6)/(x+3) * (x+3)/(6x + 8) = (8x - 6)/(6x + 8)

Hence, the simplified form of the given expression is (8x - 6)/(6x + 8). Please note that this is not the final answer but the simplified form of the original expression.