\(\dfrac{a+b}{c+d}=\dfrac{a-2b}{c-2d}\)
Suy ra: \(\left(a+b\right)\left(c-2d\right)=\left(c+d\right)\left(a-2b\right)\)
\(\Rightarrow a\left(c-2d\right)+b\left(c-2d\right)=c\left(a-2b\right)+d\left(a-2b\right)\)
\(\Rightarrow ac-2ad+bc-2bd=ac-2bc+ad-2bd\)
\(\Rightarrow ac-2ad+bc=ac-2bc+ad\)
\(\Rightarrow2ad+bc=2bc+ad\)
\(\Rightarrow2ad-ad=2bc-bc\)
\(\Rightarrow ad=bc\)
\(\Rightarrow\dfrac{a}{b}=\dfrac{c}{d}\left(đpcm\right)\)
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