问题: 我想请教一道数学题目
x x+1 x-2 x-3
--- -- --- -- --- + --- =?
x+1 x+2 x-3 x-4
解答:
x/(x+1) -(x+1)/(x+2)-(x-2)/(x-3)+(x-3)/(x-4)
=[1-1/(x+1)]-[1-1/(x+2)]-[1+1/(x-3)]+[1+1/(x-4)]
=1/(x+2)-1/(x+1)+1/(x-4)-1/(x-3)
=1/(x+2)+1/(x-4)-[1/(x+1)+1/(x-3)]
=2(x-1)[1/(x+2)(x-4)-1/(x+1)(x-3)]
=16(x-1)/(x+2)(x-4)(x+1)(x-3)
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