化简分式:(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)

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化简分式:(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)

化简分式:(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)
化简分式:(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)

化简分式:(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)
=[(x+2/x+1)-(x+3/x+2)]+[(x-5/x-4)-(x-4/x-3)]
=[(x+2)(x+2)-(x+3)(x+1)]/(x+1)(x+2)+[(x-5)(x-3)-(x-4)(x-4)]/(x-4)(x-3)
=1/(x+1)(x+2)+(-1)/(x-4)(x-3)
=-10(x-1)/(x+1)(x+2)(x-3)(x-4)
顺便鄙视验证码

-2(2x-2)

(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)
=[(x+2)²-(x+1)(x+3)]/[(x+1)(x+2)] +[(x-5)(x-3)-(x-4)²]/[(x-4)(x-3)]
=(x²+4x+4-x²-4x-3)/[(x+1)(x+2)] +(x²-8x+15-x²+8x-16)/[...

全部展开

(x+2/x+1)-(x+3/x+2)+(x-5/x-4)-(x-4/x-3)
=[(x+2)²-(x+1)(x+3)]/[(x+1)(x+2)] +[(x-5)(x-3)-(x-4)²]/[(x-4)(x-3)]
=(x²+4x+4-x²-4x-3)/[(x+1)(x+2)] +(x²-8x+15-x²+8x-16)/[(x-4)(x-3)]
=1/[(x+1)(x+2)] -1/[(x-4)(x-3)]
=[(x-4)(x-3)-(x+1)(x+2)]/[(x+1)(x+2)(x-4)(x-3)]
=(x²-7x+12-x²-3x-2)/[(x+1)(x+2)(x-4)(x-3)]
=(-10x+10)/[(x+1)(x+2)(x-4)(x-3)]
=-10(x-1)/[(x+1)(x+2)(x-4)(x-3)]

收起

有点难

10(1-x)/(x-1)(x-2)(x-3)(x-4)