分式的加减 难题巧解题
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/18 21:01:37
分式的加减 难题巧解题
x+2 x+3 x-4 x-5
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x+1 x+2 x-3 x-4
x+2 x+3 x-4 x-5
—— - —— - —— - ——
x+1 x+2 x-3 x-4
![分式的加减 难题巧解题](/uploads/image/z/18507763-19-3.jpg?t=%E5%88%86%E5%BC%8F%E7%9A%84%E5%8A%A0%E5%87%8F+%E9%9A%BE%E9%A2%98%E5%B7%A7%E8%A7%A3%E9%A2%98)
(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+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)-2
=1/[(x+1)(x+2)]-1/[(x-3)(x-4)]-2
=[1+1/(x+1)]-[1+1/(x+2)]-[1-1/(x-3)]-[1-1/(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)-2
=1/[(x+1)(x+2)]-1/[(x-3)(x-4)]-2