( + ) TH1: \(a=b\)
\(\Rightarrow\frac{a}{b}=1\) và \(\frac{a+n}{b+n}=1\)
\(\Rightarrow\frac{a}{b}=\frac{a+n}{b+n}\)
( + ) TH2: a < b
\(\frac{a}{b}=\frac{a\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+an}{b\left(b+n\right)}\)
\(\frac{a+n}{b+n}=\frac{a\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+\left(an\right)}{b\left(b+n\right)}\)
Vì a,b \(\in N\) và \(N\in N\Rightarrow an