(1/a-2+1/a+2)÷2a/a²-4a+4

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(1/a-2+1/a+2)÷2a/a²-4a+4

原式=(a+2+a-2)/(a+2)(a-2)×(a-2)²/2a
=2a/(a+2)(a-2)×(a-2)²/2a
=(a-2)/(a+2)