Have I worked this problem correctly? The direction was to solve these equations

6x^2 +7
______
3x^2 +1

x^2-X^2=x
3/6=2
7-1=6
2x6

I have no idea what your final line 2x6 is supposed to mean.

The only equation I see is

x^2-x^2=x
which is nonsense.

Better repost the original problem.

To determine if you have worked the problem correctly, let's analyze your steps:

Step 1: You are given the equations:
(6x^2 + 7) / (3x^2 + 1)

Step 2: The equation x^2 - X^2 is incorrect since X is typically used as a constant and x represents the variable. It seems like you were trying to simplify, but it is unclear what you intended to do.

Step 3: The equation 3/6 = 2 is not correct. The fraction 3/6 is equal to 0.5 or 1/2, not 2.

Step 4: The equation 7 - 1 = 6 is incorrect. The difference between 7 and 1 is equal to 6, not 6 itself.

Step 5: Finally, you multiply 2 by 6 to get 12, but it is unclear why you performed this operation or what it represents in the context of the problem.

Overall, the steps you provided do not demonstrate a clear solution to the given equations. It seems like there may have been some misunderstandings or mistakes along the way.

To correctly solve the equations (6x^2 + 7) / (3x^2 + 1), you would need to use algebraic techniques such as factoring, completing the square, or the quadratic formula, depending on the complexity of the equations. Without further information, it is not possible to determine a specific solution.