(a^2-9)/(a^2-4a+3)×（a-1)/

(a^2-9)/(a^2-4a+3)×（a-1)/a^2+4a+3

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(a^2-9)/(a^2-4a+3)×（a-1)/a^2+4a+3
=[(a-3)(a+3)/(a-3)(a-1)×(a-1)/[(a+3)(a+1)]
=(a+3)/(a-1)×(a-1)/[(a+3)(a+1)]
=1/(a+1)