Question

Cho 2 phân số \(\frac{a}{b}=\frac{c}{d}\)

Chứng minh rằng :

\(\frac{a-b}{b}=\frac{c-d}{d}\)

 

Answer 1

\(\frac{a}{b}=\frac{c}{d}\) => ad = bc

=> ad - bd = bc - bd

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

=> \(\frac{a-b}{b}=\frac{c-d}{d}\)( đpcm )

Answer 2

Ta có :  \(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\)

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

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

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