Question

So sánh a/b (b>0) và a+n/b+n (n thuộc N*)

Answer 1

\(\frac{a}{b}=\frac{a\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+an}{b\left(b+n\right)}\)

\(\frac{a+n}{b+n}=\frac{b\left(a+n\right)}{b\left(b+n\right)}=\frac{ab+bn}{b\left(b+n\right)}\)

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}

Answer 2

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 ....>...........