Question

Cho tỉ lệ thức: a/b=c/d. Chứng minh ta có: a-b/b=c-d/d

Answer 1

Đặt :

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

\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

Ta có :

\(VT=\dfrac{a-b}{b}=\dfrac{bk-b}{b}=\dfrac{b\left(k-1\right)}{b}=k-1\left(1\right)\)

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

Từ \(\left(1\right)+\left(2\right)\Leftrightarrowđpcm\)

Answer 2

Ta có:

\(\dfrac{a}{b}=\dfrac{c}{d}\\ \Leftrightarrow\dfrac{a}{b}-1=\dfrac{c}{d}-1\\ \Leftrightarrow\dfrac{a-b}{b}=\dfrac{c-d}{d}\left(đpcm\right)\)

Answer 3

Ta có:

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

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

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

Chúc bạn học tốt!