Let's first expand the numerator and denominator:

Numerator:
(x-1)(x-2)(x-3)
= (x^2 - 3x + 2)(x-3)
= x^3 - 3x^2 + 2x - 3x^2 + 9x - 6
= x^3 - 6x^2 + 11x - 6

Denominator:
(x+2)(x+1)
= x^2 + x + 2x + 2
= x^2 + 3x + 2

Now, we can simplify the expression by dividing the numerator by the denominator:

(x^3 - 6x^2 + 11x - 6) / (x^2 + 3x + 2)
= (x^2(x - 6) + 11x - 6) / (x^2 + 3x + 2)
= (x^2(x - 6) + 11x - 6) / (x + 2)(x + 1)

Therefore, the simplified expression is:

(x^2(x - 6) + 11x - 6) / (x + 2)(x + 1)