问题: h化简
(X+2/X+1 ) -(X+3/X+2)-(X-4/X-3)+(X-5/X-4)=？
解答:
(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)]
=[(x+2)-(x+1)]/[(x+1)(x+2)]+[(x-4)-(x-3)]/[(x-3)(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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