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解1\x^2+3x+2+1\x^2+5x+6+1\x^2+7x+12+1/x^2+9x+20

分类: 作业答案 • 2023-01-05 13:21:37
问题描述：

解1\x^2+3x+2+1\x^2+5x+6+1\x^2+7x+12+1/x^2+9x+20

答

原式=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+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)
=1/(x+1)-1/(x+5)
=4/(x²+6x+5)

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