Question

cho a/b=c/d chứng minh rằng a-b/a = c-d/c

 

Answer 1

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

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

\(\Rightarrow\dfrac{b}{a}-1=\dfrac{d}{c}-1\)

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

\(\Rightarrow\dfrac{a-b}{a}=\dfrac{c-d}{c}\left(đpcm\right)\)

 

Answer 2

ta có: a/b=c/d

=> ad=cb =>ac-ad=ac-cb

<=> a(c-d)=c(a-b)

=>a/a-b=c/c-d