Expression 1: x^3 + 1 / (x^3 - x^2 + x)
Expression 2: 12x / (-108x - 108)

Step 1: Factor the expressions

Expression 1: x^3 + 1 / (x^3 - x^2 + x)

Since the denominator is not factorable further, we'll leave it as it is.

Expression 2: 12x / (-108x - 108)

First, let's factor out 12x from the numerator:
12x (1 / -9(x + 1))

Step 2: Multiply the expressions

Now, we'll multiply the factored expressions:
(x^3 + 1 / (x^3 - x^2 + x)) * (12x / -9(x + 1))

Step 3: Cancel common factors (if any)

We can see that there is a common factor of (x + 1) in the denominator of the first expression and the numerator of the second expression. We'll cancel it out:
(x^3 + 1) * (12x / -9)

Step 4: Simplify

Now, let's simplify the expression further:
- (x^3 + 1) * (4x / 3)

Thus, the simplified result in factored form is: - (x^3 + 1) * (4x / 3)