计算(x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
答案:1 悬赏:40 手机版
解决时间 2021-03-05 04:14
- 提问者网友：城市野鹿
- 2021-03-04 18:22
计算(x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
最佳答案
- 五星知识达人网友：duile
- 2021-03-04 19:27
(x+2)/(x+1)-(x+3)/(x+2)-(x-4)/(x-3)+(x-5)/(x-4)
=1+1/(x+1)-1-1/(x+2)-1+1/(x-3)+1-1/(x-4)
=1/(x+1)-1/(x+2)+1/(x-3)-1/(x-4)
=1/(x+1)(x+2)-1/(x-3)(x-4)
=[(x^2-7x+12)-(x^2+3x+2)]/(x+1)(x+2)(x-3)(x-4)
=(-10x+10)/(x+1)(x+2)(x-3)(x-4)
=-10(x-1)/(x+1)(x+2)(x-3)(x-4)
=1+1/(x+1)-1-1/(x+2)-1+1/(x-3)+1-1/(x-4)
=1/(x+1)-1/(x+2)+1/(x-3)-1/(x-4)
=1/(x+1)(x+2)-1/(x-3)(x-4)
=[(x^2-7x+12)-(x^2+3x+2)]/(x+1)(x+2)(x-3)(x-4)
=(-10x+10)/(x+1)(x+2)(x-3)(x-4)
=-10(x-1)/(x+1)(x+2)(x-3)(x-4)
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