Question

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

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

Answer 1

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

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

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

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

Answer 2

Có \(\frac{a}{b}=\frac{c}{d}\)

=> \(\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\)(Tính chất dãy tỉ số bằng nhau)

=> \(\frac{b}{d}=\frac{a-b}{c-d}\)

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

Answer 3

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

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

Answer 4

Ta có:

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

\(\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-c}{b-d}\)( tính chất dãy tỉ số = nhau )

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

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

=> ĐPCM

Answer 5

Vì \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{b}-1=\frac{c}{d}-1=\frac{a}{b}-\frac{b}{b}=\frac{c}{d}-\frac{d}{d}=\frac{a-b}{b}=\frac{c-d}{d}\)

Vậy \(\frac{a-b}{b}=\frac{c-d}{d}\)