Câu 1: Giải
\(\frac{a}{b}< 1\Leftrightarrow a< b\)
\(\Leftrightarrow am< bm\)
\(\Leftrightarrow ab+am< ab+bm\)
\(\Leftrightarrow a\left(b+m\right)< b\left(a+m\right)\)
\(\Leftrightarrow\frac{a}{b}< \frac{a+m}{b+m}\left(đpcm\right)\)
Câu 2: Giải
Ta có : \(\hept{\begin{cases}\frac{437}{564}=1-\frac{127}{564}\\\frac{446}{573}=1-\frac{127}{573}\end{cases}}\)
Vì \(\frac{127}{564}>\frac{127}{573}\) nên \(\frac{437}{564}>\frac{446}{573}\)