Question

Cho tỉ lệ thức \(\dfrac{a+b}{c+d}=\dfrac{a-2b}{c-2d}\) với \(b,d\ne0\).CMR: \(\dfrac{a}{b}=\dfrac{c}{d}\)

Answer 1

\(\dfrac{a+b}{c+d}=\dfrac{a-2b}{c-2d}\Rightarrow\left(a+b\right)\left(c-2d\right)=\left(c+d\right)\left(a-2b\right)\\ ac+bc-2ad-2bd=ac+ad-2bc-2bd\\ bc-2ad=ad-2bc\\ 3bc=3ad\\ bc=ad\Rightarrow\dfrac{a}{b}=\dfrac{c}{d}\left(đpcm\right)\)

Answer 2

\(\dfrac{a+b}{c+d}=\dfrac{a-2b}{c-2d}\)

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

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

\(\Leftrightarrow2ad+ad=2bc+bc\)

\(\Leftrightarrow3ad=3bc\)

\(\Leftrightarrow ad=bc\rightarrowđpcm\)

Answer 3

Từ \(\dfrac{a+b}{c+d}=\dfrac{a-2b}{c-2d}\)

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

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

\(\Rightarrow-3ad=-3bc\)

\(\Rightarrow ad=bc\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{c}{d}\)