Question

Cho a,b,m thuộc N*

So sánh \(\frac{a+m}{b+m}\) với \(\frac{a}{b}\)

Answer 1

TH1 : a<b

\(\Rightarrow am< bm\)

\(\Rightarrow ab+am< ab+bm\Rightarrow a\left(b+m\right)< b\left(a+m\right)\)

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

TH2 : a=b

\(\Rightarrow am=bm\)

\(\Rightarrow ab+am=ab+bm\Rightarrow a\left(b+m\right)=b\left(a+m\right)\)

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

TH1 : a>b

\(\Rightarrow am>bm\)

\(\Rightarrow ab+am>ab+bm\Rightarrow a\left(b+m\right)>b\left(a+m\right)\)

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

Vậy ... ( có 3 trường hợp )