=(2a²+2a+a+1+1)/(a+1)-(a²+2a-3a-6+1)/(a+2)-(3a²-6a+2a-4-1)/(a-2)+(2a²-6a-2a+6-1)/(a-3)
=2a+1+1/(a+1)-a+3-1/(a+2)-3a-2+1/(a-2)+2a-2-1/(a-3)
=1/(a+1)-1/(a+2)+1/(a-2)-1/(a-3)
=1/(a+1)(a+2)-1/(a-2)(a-3)
=[(a-2)(a-3)-(a+1)(a+2)]/ (a+1)(a+2)(a-2)(a-3)
=(a²-5a+6-a²-3a-2)/(a+1)(a+2)(a-2)(a-3)
=(4-8a)/(a+1)(a+2)(a-2)(a-3)