Question

So sánh 2 số A và B

A=\(\frac{2017}{2018}\)+\(\frac{2018}{2019}\)                                 B=\(\frac{2017+2018}{2018+2019}\)

Answer 1

Ta có : 

\(\frac{2017}{2018}>\frac{2017}{2018+2019}\)

\(\frac{2018}{2019}>\frac{2018}{2018+2019}\)

\(\Rightarrow\frac{2017}{2018}+\frac{2018}{2019}>\frac{2017}{2018+2019}+\frac{2018}{2018+2019}\)

\(\Rightarrow\frac{2017}{2018}+\frac{2018}{2019}>\frac{2017+2018}{2018+2019}\)

\(\Rightarrow A>B\)

Chúc bạn học tốt !!!! 

Answer 2

Vì \(\frac{2017}{2018}>\frac{2017}{2018+2019}\)

Vì \(\frac{2018}{2019}>\frac{2018}{2018+2019}\)

\(\Rightarrow\frac{2017}{2018}+\frac{2018}{2019}>\frac{2017+2018}{2018+2019}\)

Answer 3

\(A=\frac{2017.2019+2018.2018}{2018.2019}=\frac{\left(2018-1\right)2019+2018\left(2019-1\right)}{2018.2019}\)
\(A=\frac{2018.2019-2019+2019.2018-2018}{2018.2019}=2-\frac{2018+2019}{2018.2019}\)
Dễ thấy \(\frac{2018+2019}{2018.2019}< 1\Rightarrow A>1\)(1)
\(2017+2018< 2018+2019\Rightarrow\frac{2017+2018}{2018+2019}< 1\Rightarrow B< 1\)(2)
Từ (1) và (2) => \(A>B\)

Answer 4

2017/2018>2017/2018+2019

Tương tự với p/s2018/2019

Suy ra 2017/2018+2018/2019>2017+2018/2018+2019=b

A>B