Theo bài ra ta có:
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)
Đặt \(\frac{a}{c}=\frac{b}{d}=k\)
\(\Rightarrow a=ck;b=dk\)
\\(\frac{a-c}{a}=\frac{ck-c}{ck}=\frac{c\cdot\left(k-1\right)}{ck}=\frac{k-1}{k}\) (1)
\(\frac{b-d}{b}=\frac{dk-d}{dk}=\frac{d\cdot\left(k-1\right)}{dk}=\frac{k-1}{k}\) (2)
Từ |(1) và (2)
\(\Rightarrow\frac{a-c}{a}=\frac{b-d}{b}\)
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ab =cd ⇒ca =db ⇒1−ca =1−db ⇒a−ca =b−db