Đáp án:

Giải thích các bước giải:

`(x+1)/2018 + (x+2)/2017 + (x+3)/2016 +( x+4)/2015=-4`

`=>(x+1)/2018 + (x+2)/2017 + (x+3)/2016 +( x+4)/2015+4=0`

`=>((x+1)/2018+1) + ((x+2)/2017 +1)+( (x+3)/2016 +1)+(( x+4)/2015+1)=0`

`=>((x+1)/2018+2018/2018) + ((x+2)/2017 +2017/2017)+( (x+3)/2016 +2016/2016)+(( x+4)/2015+2015/2015)=0`

`=>(x+2019)/2018 + (x+2019)/2017 + (x+2019)/2016 +( x+2019)/2015=0`

`=>(x+2019)(1/2018 + 1/2017 + 1/2016 +1/2015)=0`

`=>x+2019=0`

`=>x=-2019`

   $\frac{x+1}{2018}$ + $\frac{x+2}{2017}$ + $\frac{x+3}{2016}$ + $\frac{x+4}{2015}$ = -4

⇒ $\frac{x+1}{2018}$ + $\frac{x+2}{2017}$ + $\frac{x+3}{2016}$ + $\frac{x+4}{2015}$ + 4 = 0

⇒ ( $\frac{x+1}{2018}$ + 1 ) + ( $\frac{x+2}{2017}$ + 1 ) + ( $\frac{x+3}{2016}$ + 1 ) + ( $\frac{x+4}{2015}$ + 1 ) = 0

⇒ $\frac{x+2019}{2018}$ + $\frac{x+2019}{2017}$ + $\frac{x+2019}{2016}$ + $\frac{x+2019}{2015}$ = 0

⇒ ( x + 2019 ) . ( $\frac{1}{2018}$ + $\frac{1}{2017}$ + $\frac{1}{2016}$ + $\frac{1}{2015}$ ) = 0

⇒ x + 2019 = 0 ( vì $\frac{1}{2018}$ + $\frac{1}{2017}$ + $\frac{1}{2016}$ + $\frac{1}{2015}$ $\neq$ 0 )

⇒ x = - 2019