(a^3-a^2-2a)(12-a-a^2)/(a^2-2a-3)(a^4-8a^2+2a^3)
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(a^3-a^2-2a)(12-a-a^2)/(a^2-2a-3)(a^4-8a^2+2a^3)

=-a(a^2-a-2)(a^2+a-12)/(a^2-2a-3)(a^4+2a^3-8a^2)

=-a(a-2)(a+1)(a+4)(a-3)/(a-3)(a+1)(a^4+2a^3-8a^2)

=-a(a-2)(a+4)/(a^4+2a^3-8a^2)

=-a(a-2)(a+4)/[a^2(a^2+2a-8)]

=-a(a-2)(a+4)/[a^2(a+4)(a-2)]

=-1/a