So sánh: A = 2017 + 2018/2018 + 2019 và B = 2017/2018 + 2018/2019
So sánh: \(A = \frac{{2017 + 2018}}{{2018 + 2019}}\) và \(B = \frac{{2017}}{{2018}} + \frac{{2018}}{{2019}}\).
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.