一道分式计算题 {(x-2 / x+2)-(x+2/ x-2)}×(x²-2X / x²)

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一道分式计算题
{(x-2 / x+2)-(x+2/ x-2)}×(x²-2X / x²)

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