Question

So sánh hai biểu thức A và B biết rằng:

A = 2018/2019 + 2019/2020           B = (2018 + 2019)/(2019 + 2020)

Answer 1

Ta có:\(\frac{2018}{2019}\)<1\(\Rightarrow\)\(\frac{2018}{2019}\)>\(\frac{2018}{2019+2020}\)

           \(\frac{2019}{2020}\)<1\(\Rightarrow\)\(\frac{2019}{2020}\)>\(\frac{2019}{2019+2020}\)

\(\Rightarrow\)\(\frac{2018}{2019}\)+\(\frac{2019}{2020}\)>\(\frac{2018}{2019+2020}\)+\(\frac{2019}{2019+2020}\)=\(\frac{2018+2019}{2019+2020}\)

\(\Rightarrow\)A>B

Vậy A>B

Answer 2

Ta có :\(A=\frac{2018}{2019}+\frac{2019}{2020}\)

\(B=\frac{2018+2019}{2019+2020}\)

\(B=\frac{2018}{2019+2020}+\frac{2019}{2019+2020}\)

Ta thấy :

\(\frac{2018}{2019}>\frac{2018}{2019+2020}\left(2019< 2019+2020\right)\)

\(\frac{2019}{2020}>\frac{2019}{2019+2020}\left(2020< 2019+2020\right)\)

 \(\Rightarrow\frac{2018}{2019}+\frac{2019}{2020}>\frac{2018+2019}{2019+2020}\)

Vậy \(A>B\)

~ Thiên Mã ~

Answer 3

2018/2019 + 2019/2020 và
(2018 + 2019)/(2019 + 2020) = 2018 /(2019 + 2020)+ 2018)/(2018 + 2019)
do 2018/2019>2018 /(2019 + 2020)
2018/2019 >2018)/(2019 + 2020)
nên
2018/2019 + 2019/2020 > (2018 + 2019)/(2019 + 2020)