Question

so sánh

 

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

Answer 1

Ta có :  

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

Vì : 

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

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

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

Vậy \(A>B\)

Chúc bạn học tốt ~

Answer 2

cảm ơn bạn nhưng mình cần hai cách

Answer 3

Cách 2 : 

Ta có công thức : 

\(\frac{a}{b}< \frac{a+m}{b+m}\) \(\left(a< b;m>0\right)\)

\(\frac{a}{b}>\frac{a+m}{b+m}\) \(\left(a>b;m>0\right)\)

Áp dụng vào ta có : 

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

Vậy \(A>B\)