Anh Triêt cần j phải mệt thế
2)
Mình xét 2 TH sau :
TH1: \(\dfrac{a}{b}\ge1\\ \)
\(\Rightarrow a\ge b\\ \Rightarrow a.2017\ge b.2017\\ \Rightarrow2017a+ab\ge2017b+ab\\ \Rightarrow a\left(b+2017\right)\ge b\left(a+2017\right)\\ \Rightarrow\dfrac{a}{b}\ge\dfrac{a+2017}{b+2017}\)
TH2:
\(\dfrac{a}{b}< 1\\ \Rightarrow a< b\\ \Rightarrow2017.a+ab< 2017.b+ab\\ \Rightarrow a\left(b+2017\right)< b\left(a+2017\right)\\ \Rightarrow\dfrac{a}{b}< \dfrac{a+2017}{b+2017}\)