Question

Answer 1

\(\dfrac{a}{b}< \dfrac{c}{d}\\ \Leftrightarrow\dfrac{a}{b}-\dfrac{c}{d}< 0\\ \Leftrightarrow\dfrac{ad-bc}{bd}< 0\)

Vì \(b>0;d>0\)

\(\Rightarrow ad-bc< 0\\ \Leftrightarrow ab< bc\left(đpcm\right)\)

Ngược lại : \(ad< bc\)

Vì \(b>0;d>0\Rightarrow bd>0\)

Chia cả hai vế cho \(bd\)

\(ad< bc\\ \Leftrightarrow\dfrac{ad}{bd}< \dfrac{bc}{bd}\\ \Leftrightarrow\dfrac{a}{b}< \dfrac{c}{d}\left(đpcm\right)\)