Answer: To subtract the given expression, let's simplify and combine like terms.
First, let's simplify the numerator of the expression:
2x + 3x - 6 - x^2 + x - 1
= (2x + 3x + x) + (-6 - 1) - x^2
= 6x - 7 - x^2
Now, let's simplify the denominator of the expression:
x^2 + 4x + 2(x - 6)(x - 1)
= x^2 + 4x + 2(x^2 - 7x + 6)
= x^2 + 4x + 2x^2 - 14x + 12
= 3x^2 - 10x + 12
Finally, let's divide the numerator by the denominator:
(6x - 7 - x^2) / (3x^2 - 10x + 12)
At this point, we cannot simplify the expression further. Therefore, the subtraction of the given expression is:
(6x - 7 - x^2) / (3x^2 - 10x + 12)