Question

So sánh : 

\(\frac{a+m}{b+m}\)và  \(\frac{a}{b}\)

m thuộc N*

Answer 1

\(\Rightarrow\frac{a}{b}>1\)

\(\Rightarrow a>b\)

\(\Rightarrow am>bm\)

\(\Rightarrow am+ab>bm+ab\)

\(\Rightarrow a\left(m+b\right)>b\left(a+m\right)\)

\(\Rightarrow\frac{a}{b}>\frac{a+m}{b+m}\)

Answer 2

a+m/b+m  =  a/b

Answer 3

TrTrịnh dinh anh tuan sai roi

a/b<a+m/b+m 

Answer 4

Vì:             \(\frac{a}{b}\)=\(\frac{a\left(b+m\right)}{b\left(b+m\right)}\)

     và        \(\frac{a+m}{b+m}\)=\(\frac{a\left(b+m\right)}{b\left(b+m\right)}\)

Vậy có 3 trường hợp:

Answer 5

TH1: a/b < 1

=> a < b

=> a.m < b.m

=> a.m + a.b < b.m + a.b

=> a.(m + b) < b.(a + m)

=> a/b < a+m/b+m

TH2: a/b > 1

=> a > b

=> a.m > b.m

=> a.m + a.b > b.m + a.b

=> a.(m + b) > b.(a + m)

=> a/b > a+m/b+m