`\frac{x+1}{2020}+\frac{x+2}{2019}+\frac{x+3}{2018}+\frac{x+4}{2017}=-4`
`<=> \frac{x+1}{2020}+\frac{x+2}{2019}+\frac{x+3}{2018}+\frac{x+4}{2017}+4=0`
`<=>(\frac{x+1}{2020}+1)+(\frac{x+2}{2019}+1)+(\frac{x+3}{2018}+1)+(\frac{x+4}{2017}+1)=0`
`<=> \frac{x+1+2020}{2020}+\frac{x+2+2019}{2019}+\frac{x+3+2018}{2018}+\frac{x+4+2017}{2017}=0`
`<=> \frac{x+2021}{2020}+\frac{x+2021}{2019}+\frac{x+2021}{2018}+\frac{x+2021}{2017}=0`
`<=> (x+2021).(\frac{1}{2020}+\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017})=0`
`<=> `\(\left[ \begin{array}{l}x+2021=0\\\dfrac{1}{2020}+\dfrac{1}{2019}+\dfrac{1}{2018}+\dfrac{1}{2017}=0\end{array} \right.\)
Mà do `\frac{1}{2020}+\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017} \ne 0`
`=>` Vậy `S={-2021}`
