Giải các phương trình sau: k) (x − 4)/ 2 021 + (x − 3)/ 2 022 = (x − 2)/ 2 023 +( x − 1)/ 2 024 .

k) \(\frac{{x - 4}}{{2\,\,021}} + \frac{{x - 3}}{{2\,\,022}} = \frac{{x - 2}}{{2\,\,023}} + \frac{{x - 1}}{{2\,\,024}}\)

\[\left( {\frac{{x - 4}}{{2\,\,021}} - 1} \right) + \left( {\frac{{x - 3}}{{2\,\,022}} - 1} \right) = \left( {\frac{{x - 2}}{{2\,\,023}} - 1} \right) + \left( {\frac{{x - 1}}{{2\,\,024}} - 1} \right)\]

\[\frac{{x - 4 - 2\,\,021}}{{2\,\,021}} + \frac{{x - 3 - 2\,\,022}}{{2\,\,022}} = \frac{{x - 2 - 2\,\,023}}{{2\,\,023}} + \frac{{x - 1 - 2\,\,024}}{{2\,\,024}}\]

\[\frac{{x - 2\,\,025}}{{2\,\,021}} + \frac{{x - 2\,\,025}}{{2\,\,022}} - \frac{{x - 2\,\,025}}{{2\,\,023}} - \frac{{x - 2\,\,025}}{{2\,\,024}} = 0\]

\[\left( {x - 2\,\,025} \right)\left( {\frac{1}{{2\,\,021}} + \frac{1}{{2\,\,022}} - \frac{1}{{2\,\,023}} - \frac{1}{{2\,\,024}}} \right) = 0\]

Suy ra \[x - 2\,\,025 = 0\] (vì \[\frac{1}{{2\,\,021}} + \frac{1}{{2\,\,022}} - \frac{1}{{2\,\,023}} - \frac{1}{{2\,\,024}} \ne 0)\]

\(x = 2\,\,025.\)

Vậy phương trình đã cho có nghiệm \(x = 2\,\,025.\)