So sánh: A = (2017 + 2018) / (2018 + 2019)

Đề bài: So sánh: A = (2017+2018) / (2018+2019) và B = 2017/2018 + 2018/2019

Trả lời

Hướng dẫn 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.