Question

[Nguyenvananh33]

so sánh \(\frac{a}{b}\) (b>0)và    \(\frac{a+n}{b+n}\)

( n thuộc N*)

Answer 1

[Đinh Tuấn Việt]

\(\frac{a}{b}=\frac{a\left(b+n\right)}{b\left(b+n\right)}=\frac{ab+an}{b^2+bn}\)

\(\frac{a+n}{b+n}=\frac{\left(a+n\right)b}{\left(b+n\right)b}=\frac{ab+nb}{b^2+bn}\)

- Nếu a < b thì ab + an < ab + nb \(\Rightarrow\frac{a}{b}<\frac{a+n}{b+n}\)

- Nếu a > b thì ab + an > ab + nb \(\Rightarrow\frac{a}{b}>\frac{a+n}{b+n}\)

- Nếu a = b thì ab + an = ab + nb \(\Rightarrow\frac{a}{b}=\frac{a+n}{b+n}\)

Answer 2

[robert lewandoski]

Ta có;

a(b+n)=ab+an   :   b(a+n)=ab+bn

Vì b>0;n>0 nên b+n>0

Do đó:Nếu a=b thì a/b=a+n/b+n

Nếu  a>b thì ab+an>ab+bn hay a(b+n)>b(a+n) =>a/b>a+n/b+n

Nếu a<b thì ab+an<ab+bn hay a(b+n)<b(a+n) =>a/b<a+n/b+n

nhớ  cho minh ****