Question

So sánh :

A= 2016/2017 + 2017/2018

B = 2016+2017/2017+2018

hELP ME!!

Answer 1

Ta có :

\(\dfrac{2016}{2017}>\dfrac{2016}{2018}\Rightarrow A>\dfrac{2016}{2018}+\dfrac{2017}{2018}\)\(\Rightarrow A>\dfrac{2016+2017}{2018}\)

\(B=\dfrac{2016+2017}{2017+2018}=\dfrac{2016+2017}{4035}\)

Vì \(\dfrac{2016+2017}{2018}>\dfrac{2016+2017}{4035}\)

\(\Rightarrow A>B\)

~ Chúc bn học tốt ~

Answer 2

B=\(\dfrac{2016+2017}{2017+2018}\)=\(\dfrac{2016}{2017+2018}+\dfrac{2017}{2017+2018}\)

Ta có:

\(\dfrac{2016}{2017+2018}< \dfrac{2016}{2017}\)\(^{\left(1\right)}\)

\(\dfrac{2017}{2017+2018}< \dfrac{2017}{2018}\)\(^{\left(2\right)}\)

Cộng vế với vế của biểu thức (1), (2) suy ra:

\(\dfrac{2016}{2017+2018}+\dfrac{2017}{2017+2018}< \dfrac{2016}{2017}+\dfrac{2017}{2018}\)

Hay A<B