$\dfrac{x+14}{86}+\dfrac{x+15}{85}+\dfrac{x+16}{84}+\dfrac{x+17}{83}+\dfrac{x+116}{4}=0$
$↔\bigg(\dfrac{x+14}{86}+1\bigg)+\bigg(\dfrac{x+15}{85}+1\bigg)+\bigg(\dfrac{x+16}{84}+1\bigg)+\bigg(\dfrac{x+17}{83}+1\bigg)+\bigg(\dfrac{x+116}{4}-4\bigg)=0$
$↔\dfrac{x+100}{86}+\dfrac{x+100}{85}+\dfrac{x+100}{84}+\dfrac{x+100}{83}+\dfrac{x+100}{4}=0$
$↔(x+100)\bigg(\dfrac{1}{86}+\dfrac{1}{85}+\dfrac{1}{84}+\dfrac{1}{83}+\dfrac{1}{4}\bigg)=0$
$↔x+100=0$ (vì $\dfrac{1}{86}+\dfrac{1}{85}+\dfrac{1}{84}+\dfrac{1}{83}+\dfrac{1}{4}\ne 0$)
$↔x=-100$
Vậy pt có tập nghiệm $S=\{-100\}$
