[a-a/(a+1)]÷(a²-2a)/(a²-4)×(a+1)/(a²+4a+4)

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[a-a/(a+1)]÷(a²-2a)/(a²-4)×(a+1)/(a²+4a+4)[a-a/(a+1)]÷(a²-2a)/(a²-4)×(a+1)/

[a-a/(a+1)]÷(a²-2a)/(a²-4)×(a+1)/(a²+4a+4)
[a-a/(a+1)]÷(a²-2a)/(a²-4)×(a+1)/(a²+4a+4)

[a-a/(a+1)]÷(a²-2a)/(a²-4)×(a+1)/(a²+4a+4)
a²/a+1 *(a+2)/a *(a+1)/(a+2)²=a

=[a(a+1)/(a+1)-a/(a+1)]÷a(a-2)/(a+2)(a-2)×(a+1)/(a+2)²
=(a²+a-a)/(a+1)÷a/(a+2) ×(a+1)/(a+2)²
=a²/(a+1)×(a+2)/a ×(a+1)/(a+2)²
=a/(a+2)