\(\dfrac{x+1}{2023}+\dfrac{x+2}{2022}=\dfrac{x+3}{2021}+\dfrac{x+4}{2020}\\ \Leftrightarrow\dfrac{x+1}{2023}+1+\dfrac{x+2}{2022}+1=\dfrac{x+3}{2021}+1+\dfrac{x+4}{2020}+1\\ \Leftrightarrow\dfrac{x+1+2023}{2023}+\dfrac{x+2+2022}{2022}-\dfrac{x+3+2021}{2021}-\dfrac{x+4+2020}{2020}=0\\ \Leftrightarrow\left(x+2024\right)\times\left(\dfrac{1}{2023}+\dfrac{1}{2022}-\dfrac{1}{2021}-\dfrac{1}{2020}\right)=0\\ \Rightarrow x+2024=0:\left(\dfrac{1}{2023}+\dfrac{1}{2022}-\dfrac{1}{2021}-\dfrac{1}{2020}\right)\\ \Rightarrow x+2024=0\\ \Rightarrow x=-2024\)
`(x+1)/2023+(x+2)/2022=(x+3)/2021+(x+4)/2020`
`=>(x+1)/2023+1+(x+2)/2022+1=(x+3)/2021+1+(x+4)/2020+1`
`=>(x+2024)/2023+(x+2024)/2022=(x+2024)/2021+(x+2024)/2020`
`=>(x+2024)/2023+(x+2024)/2022-(x+2024)/2021-(x+2024)/2020=0`
`=>(x+2024).(1/2023+1/2022-1/2021-1/2020)=0`
Vì `1/2023+1/2022-1/2021-1/2020` `\ne` `0`
`=> x+2024=0`
`=>x=-2024`
(x+1)/2023+1+(x+2)/2020+1=(x+3)/2021+1+(x+4)/2020+1
(x+2024)/2023+(x+2024)/2020=(x+2024)/2021+(x+2024)/2020
(x+2024)/2023+(x+2024)/2020+(x+2024)/2021+(x+2024)/2020=0
(x+2024)x(1/2024 +1/2023+1/2021+1/2020)=0
=> x+2024=0
x= 0-2024
X=-2024
Vậy x=-2024
là:
