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[a²(a-3)-a²+a+6]/(a-3),
[a²(a-3)-a(a-3)-2a+6]/(a-3),
[a²(a-3)-a(a-3)-2(a-3)]/(a-3),
[(a-3)(a²-a-2)]/(a-3),
then it becomes
(a²-a-2),
a²-(2-1)a-2,
a²-2a+a-2,
a(a-2)+1(a-2),
(a-2)(a+1)
[a²(a-3)-a(a-3)-2a+6]/(a-3),
[a²(a-3)-a(a-3)-2(a-3)]/(a-3),
[(a-3)(a²-a-2)]/(a-3),
then it becomes
(a²-a-2),
a²-(2-1)a-2,
a²-2a+a-2,
a(a-2)+1(a-2),
(a-2)(a+1)
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