\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{b}{a}=\frac{d}{c}\Rightarrow1-\frac{b}{a}=1-\frac{d}{c}\)
\(\Rightarrow\frac{a-b}{a}=\frac{c-d}{c}\Rightarrow\frac{a}{a-b}=\frac{c}{c-d}\)
chuc bn hok tot
\(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\)( 1 )
Giả sử \(\frac{a}{a-b}=\frac{c}{c-d}\)thì ta có :
\(a\left(c-d\right)=c\left(a-b\right)\)
=> \(ac-ad=ca-cb\)
=> \(ad=cb\)( 2 )
Từ ( 1 ) và ( 2 ) => \(\frac{a}{a-b}=\frac{c}{c-d}\)( đpcm )