原式=(a-6)/(a+1)+12/(a+1)^2+(a+1)(a^2-1)/[(a-1)(a-2)]
=[(a-6)(a+1)+12]/(a+1)^2+(a+1)^2/(a-2)
=(a^2-5a+6)/(a+1)^2+(a+1)^2/(a-2)
=[(a^2-5a+6）（a-2)+(a+1)^4]/[(a-2)(a+1)^2]
=[a^4+4a^3+6a^2+4a+1
+a^3-5a^2+6a
-2a^2+10a-12]/[(a-2)(a+1)^2]
=(a^4+5a^3-a^2+20a-11)/[(a-2)(a+1)^2].