一道初一题,计算:x^2+2x+4-(x^3)/(x-2)?[(a^-1)-(b^-1)]/[(a^-2)+(a^-1)(b^-1)+(b^-2)]

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一道初一题,计算:x^2+2x+4-(x^3)/(x-2)?[(a^-1)-(b^-1)]/[(a^-2)+(a^-1)(b^-1)+(b^-2)]
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一道初一题,计算:x^2+2x+4-(x^3)/(x-2)?[(a^-1)-(b^-1)]/[(a^-2)+(a^-1)(b^-1)+(b^-2)]
一道初一题,计算:x^2+2x+4-(x^3)/(x-2)?
[(a^-1)-(b^-1)]/[(a^-2)+(a^-1)(b^-1)+(b^-2)]

一道初一题,计算:x^2+2x+4-(x^3)/(x-2)?[(a^-1)-(b^-1)]/[(a^-2)+(a^-1)(b^-1)+(b^-2)]
x^2+2x+4-(x^3)/(x-2)
=(x-2)(x²+2x+4)/(x-2)-x³/(x-2)
=(x³-8)/(x-2)-x³/(x-2)
=-8/(x-2)
=8/(2-x)
(a^-1)-(b^-1)/(a^-2)+(a^-1)(b^-1)+(b^-2) 分子分母同时乘以a²b²
=(ab²-a²b)/(b²+ab+a²)

原式=[(x-2)(x²+2x+4)-x³]/(x-2)
=(x³-8-x³)/(x-2)
=-8/(x-2)

x^2+2x+4-(x^3)/(x-2)
=[(x^2+2x+4)(x-2)-(x^3)]/(x-2)
=-8/(x-2)=8/(2-x)