1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20)=5/(xx+11x-708)请尽快回复

题目详情

1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20)=5/(xx+11x-708)
请尽快回复

▼优质解答

答案和解析

1/(x^2+x)+1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)+1/(x^2+9x+20)=5/(x^2+11x-708)
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=5/(x^2+11x-708)
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=5/(x^2+11x-708)
1/x-1/(x+5)=5/(x^2+11x-708)
(x+5)/x(x+5)-x/x(x+5)=5/(x^2+11x-708)
(x+5-x)/x(x+5)=5/(x^2+11x-708)
5/x(x+5)=5/(x^2+11x-708)
1/(x^2+5x)=1/(x^2+11x-708)
x^2+5x=x^2+11x-708
11x-5x=708
6x=708
x=118
经检验是x=118方程的解

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