即1/(x-5)+1/(x-9)=1/(x-6)+1/(x-8)
(2x-14)[1/(x-5)(x-9)-1/(x-6)(x-8)]=0
1/(x-5)(x-9)-1/(x-6)(x-8)≠0
所以2x-14=0
x=7
经检验,成立