Question

1/(x^2+7x)-1/(x^2+7x+6)+1/(x^2+7x+18)-1/(x^2+7x+12)=0

Answer 1

设y=x^2+7x+6

原方程化为1/(y-6)-1/y+1/(y+12)-1/(y+6)=0

12/(y^2-36)-12/(y^2+12y)=0

1/(y^2-36)=1/(y^2+12y)

y^2-36=y^2+12y

12y=-36

y=-3

x^2+7x+6=-3

x^2+7x+9=0

x=-7/2±1/2√13

经检验x=-7/2±1/2√13是原方程的解