Chứng minh rằng:
a) \( - \frac{{2023}}{{2024}} > - \frac{{2024}}{{2023}};\)
b) \(\frac{{34}}{{11}} > \frac{{26}}{9}.\)
Sử dụng tính chất bắc cầu: Nếu \(a < b\) và \(b < c\) thì \(a < c.\)
a) \( - \frac{{2023}}{{2024}} > - \frac{{2024}}{{2023}};\)
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Ta có \( - \frac{{2023}}{{2024}} > - \frac{{2024}}{{2024}}\) hay \( - \frac{{2023}}{{2024}} > - 1\)
\( - \frac{{2024}}{{2024}} > - \frac{{2024}}{{2023}}\) hay \( - 1 > - \frac{{2024}}{{2023}}\)
Suy ra \( - \frac{{2023}}{{2024}} > - \frac{{2024}}{{2023}}.\)
b) \(\frac{{34}}{{11}} > \frac{{26}}{9}.\)
Ta có \(\frac{{34}}{{11}} > \frac{{33}}{{11}}\) hay \(\frac{{34}}{{11}} > 3\)
\(\frac{{27}}{9} > \frac{{26}}{9}\) hay \(3 > \frac{{26}}{9}\)
Suy ra \(\frac{{34}}{{11}} > \frac{{26}}{9}.\)