Question

[Dũng]

CM nếu a,b \(\in\)Z;a>b ; b>0 thì \(\frac{a}{b}\)< \(\frac{a+2015}{b+2013}\)

Answer 1

[Thanh Tùng DZ]

Ta có :

\(\frac{a}{b}< \frac{2015}{2013}\)

\(\Rightarrow2013a< 2015b\)

\(\Rightarrow2013a+ab< 2015b+ab\)

\(\Rightarrow a.\left(2013+b\right)< b.\left(2015+a\right)\)

\(\Rightarrow\frac{a}{b}< \frac{a+2015}{b+2013}\)