等号右边的第一个x+3应为x+5吧?
拆项：1+1/(x+1)+1+1/(x+7)=1+1/(x+5)+1+1/(x+3)
1/(x+1)+1/(x+7)=1/(x+5)+1/(x+3)
通分：(2x+8)/[(x+1)(x+7)]=(2x+8)/[(x+5)(x+3)]
得：2x+8=0,或 (x+1)(x+7)=(x+5)(x+3)
前者得x=-4,后者展开得：7=15,矛盾
经检验,x=-4为原方程的根.