Question

giúp em vớiiiiiiiii

Answer 1

a,b \(\in\) Z, a \(\ne\) b, b > 0 

So sánh: \(\dfrac{a}{b}\) và \(\dfrac{a+2022}{b+2022}\)

  Có hai trường hợp:

+ Nếu a < b ta có:

\(\dfrac{a}{b}\) = 1 - \(\dfrac{b-a}{b}\) ;      \(\dfrac{a+2022}{b+2022}\) = 1 - \(\dfrac{b-a}{b+2022}\) 

Vì \(\dfrac{b-a}{b}\) > \(\dfrac{b-a}{b+2022}\) 

 Vậy : \(\dfrac{a}{b}\) < \(\dfrac{a+2022}{b+2022}\)

+ Nếu a > b ta có 

 \(\dfrac{a}{b}\) = 1 + \(\dfrac{a-b}{b}\);  \(\dfrac{a}{b}\) = 1 + \(\dfrac{a-b}{b+2022}\)

Vì \(\dfrac{a-b}{b}\) > \(\dfrac{a-b}{b+2022}\) 

Vậy \(\dfrac{a}{b}\) > \(\dfrac{a+2022}{b+2022}\)