Question

So sánh \(\frac{a}{b}\) ( b > 0 ) và \(\frac{a+n}{b+n}\)( n số tự nhiên khác 0 )

 

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

=> \(\frac{a}{b}=\frac{a+n}{b+n}\)

TH2: a > b

=> \(\frac{a}{b}>\frac{a+n}{b+n}\)

TH3: a < b

=> \(\frac{a}{b}