Question

Cho \(\frac{a+b}{c+d}\)=\(\frac{a-2b}{c-2d}\)(a,b,c khác 0)

CMR \(\frac{a}{b}\)=\(\frac{c}{d}\)

Answer 1

\(\frac{a+b}{c+d}=\frac{a-2b}{c-2d}\\ \Leftrightarrow\left(a+b\right)\left(c-2d\right)=\left(c+d\right)\left(a-2b\right)\)

\(\Leftrightarrow ac-2ad+bc-2bd=ac+ad-2bc-2bd\)

\(\Leftrightarrow3bc=3ad\)

\(\Leftrightarrow bc=ad\)

\(\Leftrightarrow\frac{a}{b}=\frac{c}{d}\left(đpcm\right)\)

Answer 2

\(\frac{a+b}{c+d}=\frac{a-2b}{c-2d}\Rightarrow\left(a+b\right)\left(c-2d\right)=\left(c+d\right)\left(a-2b\right)\)

=>ac-2ad+bc-2bd=ca-2bc+da-2bd

=>ac-2ad+bc-2bd-ca+2bc-da+2bd=0

=>-3ad+3bc=0

=>3ad=3bc

=>ad=bc

=>a/b=c/d