分式加减法求解 要过程
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1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)
=1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+1/(x-4)-1/(x-3)+1/(x-5)-1/(x-4)
=1/(x-5)
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)
=1/(x-1)+1/(x-2)[1/(x-1)+1/(x-3)]+1/(x-4)[1/(x-3)+1/(x-5)]
=1/(x-1)+1/(x-2)[(x-3+x-1)/(x-1)(x-3)]+1/(x-4)[(x-5+x-3)/(x-3)(x-5)]
=1/(x-1)+1/(x-2)*2(x-2)/(x-1)(x-3)+1/(x-4)*2(x-4)/(x-3)(x-5)
=1/(x-1)+2/(x-1)(x-3)+2/(x-3)(x-5)
=1/(x-1)+2/(x-3)[1/(x-1)+1/(x-5)]
=1/(x-1)+2/(x-3)[(x-5+x-1)/(x-1)(x-5)]
=1/(x-1)+2/(x-3)*2(x-3)/(x-1)(x-5)
=1/(x-1)+4/(x-1)(x-5)
=(x-5+4)/(x-1)(x-5)
=1/(x-5)
=1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+1/(x-4)-1/(x-3)+1/(x-5)-1/(x-4)
=1/(x-5)
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)
=1/(x-1)+1/(x-2)[1/(x-1)+1/(x-3)]+1/(x-4)[1/(x-3)+1/(x-5)]
=1/(x-1)+1/(x-2)[(x-3+x-1)/(x-1)(x-3)]+1/(x-4)[(x-5+x-3)/(x-3)(x-5)]
=1/(x-1)+1/(x-2)*2(x-2)/(x-1)(x-3)+1/(x-4)*2(x-4)/(x-3)(x-5)
=1/(x-1)+2/(x-1)(x-3)+2/(x-3)(x-5)
=1/(x-1)+2/(x-3)[1/(x-1)+1/(x-5)]
=1/(x-1)+2/(x-3)[(x-5+x-1)/(x-1)(x-5)]
=1/(x-1)+2/(x-3)*2(x-3)/(x-1)(x-5)
=1/(x-1)+4/(x-1)(x-5)
=(x-5+4)/(x-1)(x-5)
=1/(x-5)
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