So sánh: A = 2017 + 2018/2018 + 2019 và B = 2017/2018 + 2018/2019

Trả lời

Lời giải

Ta có: $A = \frac{{2017 + 2018}}{{2018 + 2019}}$$= \frac{{2017}}{{2018 + 2019}} + \frac{{2018}}{{2018 + 2019}}$.

Ta thấy $\frac{{2017}}{{2018 + 2019}} < \frac{{2017}}{{2018}}$; $\frac{{2018}}{{2018 + 2019}} < \frac{{2018}}{{2019}}$

Nên $\frac{{2017}}{{2018 + 2019}} + \frac{{2018}}{{2018 + 2019}} < \frac{{2017}}{{2018}} + \frac{{2018}}{{2019}}$.

Do đó A < B.