Question

解方程1/[x(x+3)]+1/[(x+3)(x+6)]+1/[(x+6)(x+9)]=3/(x平方+1)

Answer 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