1/(x+5)+1/(x+8)=1/(x+6)+1/(x+7)
(2x+13)/(x+5)(x+8)=(2x+13)/(x+6)(x+7)
(2x+13)[(x+6)(x+7)-(x+5)(x+8)]=0
(2x+13)*2=0
x=-13/2