\(\frac{a}{b}=\frac{a\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+an}{b\left(b+n\right)}\)
\(\frac{a+n}{b+n}=\frac{b\left(a+n\right)}{b\left(b+n\right)}=\frac{ab+bn}{b\left(b+n\right)}\)
TH1: a = b
=> ab+an = ab+bn
=> \(\frac{a}{b}=\frac{a+n}{b+n}\)
TH2: a > b
=> ab+an > ab+bn
=> \(\frac{a}{b}>\frac{a+n}{b+n}\)
TH3: a < b
=> ab+an < ab+bn
=> \(\frac{a}{b}
a/b=ab+an/b^2+bn
a+n/b+n=ab+bn/b^2+bn
xảy ra ba trường hợp
a<b thi a/b<a+n/b+n
a=b thì.....=...........
a>b thì ....>...........