作业帮解方程1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 12:08:50
![解方程1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)](/uploads/image/z/579818-2-8.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B1%2F%5Bx%28x%2B3%29%5D%2B1%2F%5B%28x%2B3%29%28x%2B6%29%5D%2B1%2F%5B%28x%2B6%29%28x%2B9%29%5D%3D3%2F%28x%E5%B9%B3%E6%96%B9%2B1%29)
解方程1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)
解方程1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)
解方程1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)
1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)
1/3[1/x-1/(x+3)]+1/3[1/(x+3)-1/(x+6)]+1/3[1/(x+6)-1/(x+9)]=3/(x^2+1)
1/3[1/x-1/(x+3)+1/(x+3)-1/(x+6)+1/(x+6)-1/(x+9)]=3/(x^2+1)
1/3[1/x-1/(x+9)]=3/(x^2+1)
1/3(x+9-x)/x(x+9)=3/(x^2+1)
3/x(x+9)=3/(x^2+1)
x(x+9)=x^2+1
x^2+9x=x^2+1
9x=1
x=1/9
检验：X=1/9是方程的根