解方程：1⼀x(x+3)+1⼀(x+3)(x+6)-1⼀3x=1

1/x(x+3)+1/(x+3)(x+6)-1/3x=1
3(x+6)+3x-(x+3)(x+6)=3x(x+3)(x+6)
3x+18+3x-x^2-9x-18=3x(x^2+9x+18)
-x^2-3x=3x^3+27x^2+54x
3x^3+28x^2+57x=0
x(3x^2+28x^+57)=0
x1=0 (3x+19)(x+3)=0
x2=-19/3 x=-3
经验证x1=0为增根
x2=-19/3 x=-3

等式两边同乘以3x(x+3)(x+6)得
3(x+6)+3x-(x+3)(x+6)=3x(x+3)(x+6)
3(2x+6)-(x+3)(x+6)=-(x+3)x=3x(x+3)(x+6)
根据定义域,x≠0，(x+3)≠0，(x+6)≠0
所以上式化为-1=3(x+6)
解得x=-19/3

把各个因式拆开，得[1/x-1/(x+3)]×1/3+[1/(x+3)-1/(x+6)]×1/3-1/3x=1
整理得1/x-1/(x+3)+1/(x+3)-1/(x+6)=3
1/x-1/(x+6)=3

x+6-x=3x(x+6)
x^2+6x-2=0
x=3+√11或3-√11