\(\frac{a}{b}>\frac{c}{d}\)
\(\Rightarrow ad>bc\)
\(\Rightarrow ad+ab>bc+ab\)
\(\Rightarrow a\left(b+d\right)>b\left(a+c\right)\)
\(\Rightarrow\frac{a}{b}>\frac{a+c}{b+d}\)( 1 )
\(\Rightarrow ad+cd>bc+cd\)
\(\Rightarrow d\left(a+c\right)>c\left(b+d\right)\)
\(\Rightarrow\frac{a+c}{b+d}>\frac{c}{d}\)( 2 )
Từ ( 1 ) và ( 2 ) \(\Rightarrow\frac{a}{b}>\frac{a+c}{b+d}>\frac{c}{d}\)