To solve the equation, we first need to simplify it:

6x - x^2 - 6 - (-2x) - 3 / x - 1 = 1
6x - x^2 - 6 + 2x - 3 / x - 1 = 1
-x^2 + 8x - 9 / x - 1 = 1

Now, multiply both sides by (x - 1) to clear the fraction:

(-x^2 + 8x - 9) = (x - 1)

Next, move all terms to one side of the equation:

-x^2 + 8x - 9 - x + 1 = 0
-x^2 + 7x - 8 = 0

Now, we can factorize the quadratic equation:

(x - 8)(x + 1) = 0

From this, we find the values of x:

x = 8
x = -1

Therefore, the solutions to the equation are x = 8 and x = -1.