\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{b}{a}=\dfrac{d}{c}\)
Ta có:
\(1:\dfrac{a}{a+b}=\dfrac{a+b}{a}=1+\dfrac{b}{a}\)
\(1:\dfrac{c}{c+d}=\dfrac{c+d}{c}=1+\dfrac{d}{c}\)
Vì \(\dfrac{b}{a}=\dfrac{d}{c}\) nên \(1+\dfrac{b}{a}=1+\dfrac{d}{c}\). \(\Rightarrow\) \(1:\dfrac{a}{a+b}=1:\dfrac{c}{c+d}\). \(\Rightarrow\) \(\dfrac{a}{a+b}=\dfrac{c}{c+d}\)
\(\Rightarrow\) ĐPCM
