分式化简 [(x^2-4/x^2-4x+4)-(x-2/x+2)]/(x/x-2)

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分式化简 [(x^2-4/x^2-4x+4)-(x-2/x+2)]/(x/x-2)
分式化简 [(x^2-4/x^2-4x+4)-(x-2/x+2)]/(x/x-2)

分式化简 [(x^2-4/x^2-4x+4)-(x-2/x+2)]/(x/x-2)
{[(x²-4)/(x²-4x+4)]-(x-2)/(x+2)}/[x/(x-2)]
=[(x+2)(x-2)/(x-2)²-(x-2)/(x+2)][(x-2)/x]
=[(x+2)/(x-2)-(x-2)/(x+2)][(x-2)/x]
=[(x+2)/(x-2)][(x-2)/x]-[(x-2)/(x+2)][(x-2)/x]
=(x+2)/x-(x-2)²/x(x+2)
=[(x+2)²-(x-2)²]/x(x+2)
=[(x+2)-(x-2)][(x+2)+(x-2)]/x(x+2)
=8x/x(x+2)
=8/(x+2)
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