(a^2-4/a^-4a+4-1/a-2)÷a+1/a+2

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(a^2-4/a^-4a+4-1/a-2)÷a+1/a+2

(a^2-4/a^-4a+4-1/a-2)÷a+1/a+2
(a^2-4/a^-4a+4-1/a-2)÷a+1/a+2

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

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