化简1/（x²-4x+4）-x/(x²-4)+1/(2x+4)
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1/（x²-4x+4）-x/(x²-4)+1/(2x+4)
=1/(x-2)²-x/[(x-2)(x+2)]+1/2(x+2)
通分
=[2(x+2)-2x(x-2)+(x-2)²]/[2(x-2)²(x+2)]
=[2x+4-2x²+4x+x²-4x+4]/[2(x-2)²(x+2)]
=[-x²+2x+8]/[2(x-2)²(x+2)]
=-(x-4)(x+2)/[2(x-2)²(x+2)]
=-(x-4)/[2(x-2)²]
=1/(x-2)²-x/[(x-2)(x+2)]+1/2(x+2)
通分
=[2(x+2)-2x(x-2)+(x-2)²]/[2(x-2)²(x+2)]
=[2x+4-2x²+4x+x²-4x+4]/[2(x-2)²(x+2)]
=[-x²+2x+8]/[2(x-2)²(x+2)]
=-(x-4)(x+2)/[2(x-2)²(x+2)]
=-(x-4)/[2(x-2)²]
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1/(x-2)^2-x/(x-2)(x+2)+1/2(x+2)
(2x+4-2x(x-2)+(x-2)^2)/2(x-2)^2(x+2)
=(2x+4-2x^2+4x+x^2-4x+4)/2(x-2)^2(x+2)
=(-x^2+2x+8)/2(x-2)^2(x+2)
=-(x-4)(x+2)/2(x-2)(x+2)
=-(x-4)/2(x-2)
=(4-x)/2(x-2)
(2x+4-2x(x-2)+(x-2)^2)/2(x-2)^2(x+2)
=(2x+4-2x^2+4x+x^2-4x+4)/2(x-2)^2(x+2)
=(-x^2+2x+8)/2(x-2)^2(x+2)
=-(x-4)(x+2)/2(x-2)(x+2)
=-(x-4)/2(x-2)
=(4-x)/2(x-2)
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