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原式=(x²+3x+9)/(x-3)(x²+3x+9)-6x/x(x+3)(x-3)+(x-1)/2(x+3)
=1/(x-3)-6/(x+3)(x-3)+(x-1)/2(x+3)
=[2(x+3)-12+(x-1)(x-3)]/[2(x+3)(x-3)]
=(2x+6-12+x²-4x+3)/[2(x+3)(x-3)]
=(x²-2x-3)/[2(x+3)(x-3)]
=(x-3)(x+1)/[2(x+3)(x-3)]
=(x+1)/(2x+6)
=1/(x-3)-6/(x+3)(x-3)+(x-1)/2(x+3)
=[2(x+3)-12+(x-1)(x-3)]/[2(x+3)(x-3)]
=(2x+6-12+x²-4x+3)/[2(x+3)(x-3)]
=(x²-2x-3)/[2(x+3)(x-3)]
=(x-3)(x+1)/[2(x+3)(x-3)]
=(x+1)/(2x+6)
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