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