TH1: x<2019

=>x-2019<0; x-2021<0; x-2023<0

Phương trình sẽ trở thành:

2019-x+2021-x+2023-x=4

=>6063-3x=4

=>3x=6063-4=6059

=>\(x=\frac{6059}{3}\) (loại)

TH2: 2019<=x<2021

=>x-2019>=0; x-2021<0; x-2023<0

Phương trình sẽ trở thành:

x-2019+2021-x+2023-x=4

=>-x+2025=4

=>-x=-2021

=>x=2021(loại)

TH3: 2021<=x<2023

=>x-2019>0; x-2021>=0; x-2023<0

Phương trình sẽ trở thành:

x-2019+x-2021+2023-x=4

=>x-2017=4

=>x=2021(nhận)

TH4: x>=2023

=>x-2019>0; x-2021>0; x-2023>=0

Phương trình sẽ trở thành:

x-2019+x-2021+x-2023=4

=>3x-6063=4

=>3x=6067

=>\(x=\frac{6067}{3}\) (loại)

Vậy: x=2021

TH1: x<2019

=>x-2019<0; x-2021<0; x-2023<0

Phương trình sẽ trở thành:

2019-x+2021-x+2023-x=4

=>6063-3x=4

=>3x=6063-4=6059

=>\(x=\frac{6059}{3}\) (loại)

TH2: 2019<=x<2021

=>x-2019>=0; x-2021<0; x-2023<0

Phương trình sẽ trở thành:

x-2019+2021-x+2023-x=4

=>-x+2025=4

=>-x=-2021

=>x=2021(loại)

TH3: 2021<=x<2023

=>x-2019>0; x-2021>=0; x-2023<0

Phương trình sẽ trở thành:

x-2019+x-2021+2023-x=4

=>x-2017=4

=>x=2021(nhận)

TH4: x>=2023

=>x-2019>0; x-2021>0; x-2023>=0

Phương trình sẽ trở thành:

x-2019+x-2021+x-2023=4

=>3x-6063=4

=>3x=6067

=>\(x=\frac{6067}{3}\) (loại)

Vậy: x=2021

4

4

2021 x 2021 - 2019 x 2023 

= (2019 +2) x ( 2023 -2) - 2019 x 2023

= 2019 x 2023 - 2 x 2019 + 2 x 2023 - 4 - 2019 x 2023

= ( 2019 x 2023 - 2019 x 2023) + 2 x ( 2023 - 2019) - 4

= 0 + 2 x 4 - 4

= 8 - 4

 = 4

2021 x 2021 - 2019 x 2023 

= (2019 +2) x ( 2023 -2) - 2019 x 2023

= 2019 x 2023 - 2 x 2019 + 2 x 2023 - 4 - 2019 x 2023

= ( 2019 x 2023 - 2019 x 2023) + 2 x ( 2023 - 2019) - 4

= 0 + 2 x 4 - 4

= 8 - 4

 = 4

\(\frac{x+1}{2019}+\frac{x+2}{2018}+\frac{x+3}{2017}=\frac{x-1}{2021}+\frac{x-2}{2022}+\frac{x-3}{2023}\)

\(\Leftrightarrow\left(\frac{x+1}{2019}+1\right)+\left(\frac{x+2}{2018}+1\right)+\left(\frac{x+3}{2017}+1\right)=\left(\frac{x-1}{2021}+1\right)+\left(\frac{x-2}{2022}+1\right)+\left(\frac{x-3}{2023}+1\right)\)

\(\Leftrightarrow\left(\frac{x+1+2019}{2019}\right)+\left(\frac{x+2+2018}{2018}\right)+\left(\frac{x+3+2017}{2017}\right)=\left(\frac{x-1+2021}{2021}\right)+\left(\frac{x-2+2022}{2022}\right)+\left(\frac{x-3+2023}{2023}\right)\)

\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}=\frac{x+2020}{2021}+\frac{x+2020}{2022}+\frac{x+2020}{2023}\)

\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}-\frac{x+2020}{2021}-\frac{x+2020}{2022}-\frac{x+2020}{2023}=0\)

\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\right)=0\)

Vì \(\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\ne0\)

=> x + 2020 = 0

=> x = -2020

            Bài làm :

Ta có :

\(\frac{x+1}{2019}+\frac{x+2}{2018}+\frac{x+3}{2017}=\frac{x-1}{2021}+\frac{x-2}{2022}+\frac{x-3}{2023}\)

\(\Leftrightarrow\left(\frac{x+1}{2019}+1\right)+\left(\frac{x+2}{2018}+1\right)+\left(\frac{x+3}{2017}+1\right)=\left(\frac{x-1}{2021}+1\right)+\left(\frac{x-2}{2022}+1\right)+\left(\frac{x-3}{2023}+1\right)\)

\(\Leftrightarrow\left(\frac{x+1+2019}{2019}\right)+\left(\frac{x+2+2018}{2018}\right)+\left(\frac{x+3+2017}{2017}\right)=\left(\frac{x-1+2021}{2021}\right)+\left(\frac{x-2+2022}{2022}\right)+\left(\frac{x-3+2023}{2023}\right)\)

\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}=\frac{x+2020}{2021}+\frac{x+2020}{2022}+\frac{x+2020}{2023}\)

\(\Leftrightarrow\frac{x+2020}{2019}+\frac{x+2020}{2018}+\frac{x+2020}{2017}-\frac{x+2020}{2021}-\frac{x+2020}{2022}-\frac{x+2020}{2023}=0\)

\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\right)=0\)

 \(\text{Vì : }\frac{1}{2019}+\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2021}-\frac{1}{2022}-\frac{1}{2023}\ne0\)

\(\Rightarrow x+2020=0\Leftrightarrow x=-2020\)

Vậy x=-2020

\(\dfrac{x-1}{2019-2}+\dfrac{x-3}{2019}=\dfrac{x-5}{2021}+\dfrac{x-7}{2023}\)

\(\Leftrightarrow\dfrac{x-1}{2017}+\dfrac{x-3}{2019}=\dfrac{x-5}{2021}+\dfrac{x-7}{2023}\)

\(\Leftrightarrow\left(\dfrac{x-1}{2017}+1\right)+\left(\dfrac{x-3}{2019}+1\right)=\left(\dfrac{x-5}{2021}+1\right)+\left(\dfrac{x-7}{2023}+1\right)\)

=>x+2016=0

hay x=-2016