方程左边1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20)对分母因式分解得
1/x（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/(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)
=1/x-1/(x+5)
=5/x(x+5)
所以原方程可化简得
5/x(x+5)=5/(xx+11x-708）
方程两边同乘以最简公分母得xx+11x-708=x(x+5)
解得x=118
经检验得：x=118是原方程的解