Question

So sánh

A=\(\dfrac{2016^9+3}{2016^9-1}\) B=\(\dfrac{2016^9}{2016^9-4}\)

Answer 1

Ta có :

\(A=\dfrac{2016^9+3}{2016^9-1}=\dfrac{2016^9-1+4}{2016^9-1}=\dfrac{2016^9-1}{2016^9-1}+\dfrac{4}{2016^9-1}=1+\dfrac{4}{2016^9-1}\)

\(B=\dfrac{2016^9}{2016^9-4}=\dfrac{2016^9-4+4}{2016^9-4}=\dfrac{2016^9-4}{2016^9-4}+\dfrac{4}{2016^9-4}=1+\dfrac{4}{2016^9-4}\)

Vì \(1+\dfrac{4}{2016^9-1}< 1+\dfrac{4}{2016^9-4}\Rightarrow A< B\)