\(\frac{a}{b}< \frac{a+n}{b+n}\) \(\left(1\right)\)
\(\Leftrightarrow a\left(b+n\right)< b\left(a+n\right)\)
\(\Leftrightarrow ab+an< ab+bn\)
\(\Leftrightarrow an< bn\)
\(Do.a< b\)nên an<bn\(\Rightarrow\)(1)
\(\frac{a}{b}>\frac{a+n}{b+n}\)\(\left(2\right)\)
\(\Leftrightarrow a\left(b+n\right)>b\left(a+n\right)\)
\(\Leftrightarrow ab+an>ab+bn\)
\(\Leftrightarrow an>bn\)
Do a>b nên \(\Rightarrow\)(2)