các bạn ơi giúp mình với nhé

Bài 18: a) Ta có: \[ \frac{x-23}{24} + \frac{x-23}{25} = \frac{x-23}{26} + \frac{x-23}{27} \] Nhân cả hai vế với 24 × 25 × 26 × 27, ta được: \[ (x-23)(25 \times 26 \times 27) + (x-23)(24 \times 26 \times 27) = (x-23)(24 \times 25 \times 27) + (x-23)(24 \times 25 \times 26) \] Rút gọn, ta có: \[ (x-23)(25 \times 26 \times 27 + 24 \times 26 \times 27) = (x-23)(24 \times 25 \times 27 + 24 \times 25 \times 26) \] Do đó: \[ (x-23)(26 \times 27(25 + 24)) = (x-23)(24 \times 25(27 + 26)) \] \[ (x-23)(26 \times 27 \times 49) = (x-23)(24 \times 25 \times 53) \] \[ (x-23)(26 \times 27 \times 49 - 24 \times 25 \times 53) = 0 \] Vậy: \[ x - 23 = 0 \quad \text{hoặc} \quad 26 \times 27 \times 49 - 24 \times 25 \times 53 = 0 \] Ta thấy \(26 \times 27 \times 49 - 24 \times 25 \times 53\) không bằng 0, do đó: \[ x - 23 = 0 \implies x = 23 \] b) Ta có: \[ \left(\frac{x+2}{98} + 1\right) + \left(\frac{x+3}{97} + 1\right) = \left(\frac{x+4}{96} + 1\right) + \left(\frac{x+5}{95} + 1\right) \] Nhân cả hai vế với 98 × 97 × 96 × 95, ta được: \[ (x+2)(97 \times 96 \times 95) + (x+2)(98 \times 96 \times 95) + (x+3)(98 \times 96 \times 95) + (x+3)(98 \times 97 \times 95) = (x+4)(98 \times 97 \times 95) + (x+4)(98 \times 97 \times 96) + (x+5)(98 \times 97 \times 96) + (x+5)(98 \times 97 \times 96) \] Rút gọn, ta có: \[ (x+2)(97 \times 96 \times 95 + 98 \times 96 \times 95) + (x+3)(98 \times 96 \times 95 + 98 \times 97 \times 95) = (x+4)(98 \times 97 \times 95 + 98 \times 97 \times 96) + (x+5)(98 \times 97 \times 96 + 98 \times 97 \times 95) \] \[ (x+2)(96 \times 95(97 + 98)) + (x+3)(98 \times 95(96 + 97)) = (x+4)(98 \times 95(97 + 96)) + (x+5)(98 \times 96(97 + 95)) \] \[ (x+2)(96 \times 95 \times 195) + (x+3)(98 \times 95 \times 193) = (x+4)(98 \times 95 \times 193) + (x+5)(98 \times 96 \times 192) \] \[ (x+2)(96 \times 95 \times 195 - 98 \times 95 \times 193) + (x+3)(98 \times 95 \times 193 - 98 \times 96 \times 192) = 0 \] Vậy: \[ x + 2 = 0 \quad \text{hoặc} \quad 96 \times 95 \times 195 - 98 \times 95 \times 193 = 0 \] Ta thấy \(96 \times 95 \times 195 - 98 \times 95 \times 193\) không bằng 0, do đó: \[ x + 2 = 0 \implies x = -2 \] c) Ta có: \[ \frac{x+1}{2024} + \frac{x+2}{2023} = \frac{x+3}{2022} + \frac{x+4}{2021} \] Nhân cả hai vế với 2024 × 2023 × 2022 × 2021, ta được: \[ (x+1)(2023 \times 2022 \times 2021) + (x+2)(2024 \times 2022 \times 2021) = (x+3)(2024 \times 2023 \times 2021) + (x+4)(2024 \times 2023 \times 2022) \] Rút gọn, ta có: \[ (x+1)(2023 \times 2022 \times 2021 + 2024 \times 2022 \times 2021) + (x+2)(2024 \times 2022 \times 2021 + 2024 \times 2023 \times 2021) = (x+3)(2024 \times 2023 \times 2021 + 2024 \times 2023 \times 2022) + (x+4)(2024 \times 2023 \times 2022 + 2024 \times 2023 \times 2021) \] \[ (x+1)(2022 \times 2021(2023 + 2024)) + (x+2)(2024 \times 2021(2022 + 2023)) = (x+3)(2024 \times 2021(2023 + 2022)) + (x+4)(2024 \times 2022(2023 + 2021)) \] \[ (x+1)(2022 \times 2021 \times 4047) + (x+2)(2024 \times 2021 \times 4045) = (x+3)(2024 \times 2021 \times 4045) + (x+4)(2024 \times 2022 \times 4044) \] \[ (x+1)(2022 \times 2021 \times 4047 - 2024 \times 2021 \times 4045) + (x+2)(2024 \times 2021 \times 4045 - 2024 \times 2022 \times 4044) = 0 \] Vậy: \[ x + 1 = 0 \quad \text{hoặc} \quad 2022 \times 2021 \times 4047 - 2024 \times 2021 \times 4045 = 0 \] Ta thấy \(2022 \times 2021 \times 4047 - 2024 \times 2021 \times 4045\) không bằng 0, do đó: \[ x + 1 = 0 \implies x = -1 \] Đáp số: a) \(x = 23\) b) \(x = -2\) c) \(x = -1\)