(x+6)/(x+5)
=(x+5+1)/(x+5)
=(x+5)/(x+5)+1/(x+5)
=1+1/(x+5)
同理
1+1/(x+5)+1+1/(x+9)=1+1/(x+7)+1+1/(x+8)
通分
(2x+14)/(x²+14x+45)=(2x+14)/(x²+14x+56)
(2x+14)[1/(x²+14x+45)-1/(x²+14x+56)]=0
因为x²+14x+45≠x²+14x+56
所以1/(x²+14x+45)-1/(x²+14x+56)≠0
所以2x+14=0
x=-7
经检验,x=-7是方程的根