\(\frac{a}{b}=\frac{a\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+an}{b\left(b+n\right)}\)
\(\frac{a+n}{b+n}=\frac{b\left(a+n\right)}{b\left(b+n\right)}=\frac{ab+bn}{b\left(b+n\right)}\)
TH1: a = b
=> \(\frac{a}{b}=\frac{a+n}{b+n}\)
TH2: a > b
=> \(\frac{a}{b}>\frac{a+n}{b+n}\)
TH3: a < b
=> \(\frac{a}{b}