通分
(x+5+x+8)/(x+5)(x+8)=(x+6+x+7)/(x+6)(x+7)
(2x+13)/(x^2+13x+40)=(2x+13)/(x^2+13x+42)
(2x+13)[1/(x^2+13x+40)-1/(x^2+13x+42)]=0
因为x^2+13x+40不等于x^2+13x+42
所以1/(x^2+13x+40)-1/(x^2+13x+42)=0不成立
所以2x+13=0
x=-13/2
经检验,x=-13/2是方程的解