1/x-5 1/x-6 = 1/x-8 - 1/x-9

1/(x-5)+1/(x-9)=1/(x-6)+1/(x+8)
通分
(2x-14)/(x²-14x+45)=(2x-14)/(x²-14x+48)
(2x-14)[1/(x²-14x+45)-1/(x²-14x+48)]=0
x²-14x+45≠x²-14x+48
所以1/(x²-14x+45)-1/(x²-14x+48)≠0
所以2x-14=0
x=7
经检验,x=7是方程的解