1/(x+1)+1/(x-5)=1/(x+3)+1/(x-7)
通分
(x-5+x+1)/(x+1)(x-5)=(x-7+x+3)/(x+3)(x-7)
(2x-4)/(x²-4x-5)=(2x-4)/(x²-4x-21)
(2x-4)[1/(x²-4x-5)-1/(x²-4x-21)]=0
x²-4x-5≠x²-4x-21
所以中括号不等于0
所以2x-4=0
x=2
经检验,x=2是方程的解