To simplify the expression, we first need to find a common denominator for both fractions:
(a-1)/(a+2) = (a-1)(a^2+3a+2)/(a+2)(a^2+3a+2) = (a^3+2a^2-3a-2)/(a^3+5a^2+6a+4)

(1-a)/(a^2+3a+2) = (1-a)/(a+2)(a+1) = (1-a)/(a^2+3a+2)

Now we can rewrite the expression with a common denominator:
(a^3+2a^2-3a-2)/(a^3+5a^2+6a+4) - (1-a)/(a^3+5a^2+6a+4)

Now, combine the numerators:
(a^3+2a^2-3a-2 - 1 + a)/(a^3+5a^2+6a+4)

Simplify the numerator:
a^3+2a^2-3a-2-1+a = a^3+2a^2-3a-1

Now, rewrite the expression:
(a^3+2a^2-3a-1)/(a^3+5a^2+6a+4)