Cho a, b, m thuộc N*. Hãy so sánh a+m / b+m với a/b

* Hướng dẫn giải

$\frac{a+m}{b+m}=\frac{\left(a+m\right).b}{\left(b+m\right).b}=\frac{ab+mb}{\left(b+m\right).b};$$\frac{a}{b}=\frac{a\left(b+m\right)}{\left(b+m\right).b}=\frac{ab+am}{\left(b+m\right).b}$

Do $a>b\Rightarrow am>bm\Rightarrow ab+mb>ab+am$$\Rightarrow \frac{a+m}{b+m}>\frac{a}{b}$