Question

[Lạc Chỉ]

Cho a/b = c/d. CMR a - b/ a = c - d/ c

Answer 1

[Nguyễn Thị Ngọc Ánh]

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

\(\Rightarrow1-\frac{b}{a}=1-\frac{d}{c}\)

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

hc tốt nha

Answer 2

[Xyz OLM]

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

\(\Rightarrow a=bk;=dk\)

Khi đó : \(\frac{a-b}{a}=\frac{bk-b}{bk}=\frac{b\left(k-1\right)}{bk}=\frac{k-1}{k}\left(1\right)\) 

\(\frac{c-d}{c}=\frac{dk-d}{dk}=\frac{d\left(k-1\right)}{dk}=\frac{k-1}{k}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\frac{a-b}{a}=\frac{c-d}{c}\left(\text{đpcm}\right)\)