计算,(a²-1)/(a²+4a+4)÷(a+1)/(a+2)

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计算,
(a²-1)/(a²+4a+4)÷(a+1)/(a+2)

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

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