[1/(a^-a+1)-(1-a)/(a^3-1)]/{(a^4-a^2-2) /[(a^6-1)-(a^4+a^2+1
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化简[1/(a²-a+1)-(1-a)/(a³-1)]/{(a⁴-a²-2) /[(a⁶-1)-(a⁴+a²+1)]}
原式=[1/(a²-a+1)+(a-1)/(a-1)(a²+a+1)]×{[(a²-1)(a⁴+a²+1)-(a⁴+a²+1)]/(a⁴-a²-2)]}
=[1/(a²-a+1)+1/(a²+a+1)][(a⁴+a²+1)(a²-2)/(a⁴-a²-2)]
={2(a²+1)/[(a²+1)-a][(a²+1)+a]}[(a⁴+a²+1)(a²-2)/(a⁴-a²-2)]
={2(a²+1)/[(a²+1)²-a²]}[(a⁴+a²+1)(a²-2)/(a⁴-a²-2)]
=[2(a²+1)/(a⁴+a²+1)][a⁴+a²+1)(a²-2)/(a⁴-a²-2)]
=2(a²+1)(a²-2)/(a⁴-a²-2)
=2(a⁴-a²-2)/(a⁴-a²-2)
=2
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