(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a_2)/(b^2+b-6)

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(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a_2)/(b^2+b-6)

(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a_2)/(b^2+b-6)
(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a_2)/(b^2+b-6)

(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a_2)/(b^2+b-6)
(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a_2)/(b^2+b-6)
=(a^2b-ab-a+1)/(ab^2+3ab-b-3)×(b^2+b-6)/(a^2+a_2)
=(a^2b-ab-a+1)(b^2+b-6)/(ab^2+3ab-b-3)×(a^2+a_2)
=(ab-1)(a-1)(b+3)(b-2)/(ab-1)(b+3)(a+2)(a-1)
=(b-2)/(b+3)

(a^2b-ab-a+1)/(ab^2+3ab-b-3)÷(a^2+a-2)/(b^2+b-6)
=(ab-1)(a-1)/(ab-1)(b+3)×(b+3)(b-2)/(a+2)(a-1)
=(a-1)/(b+3)×(b+3)(b-2)/(a+2)(a-1)
=(b-2)/(a+2)