Question

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

Answer 1

Gọi \(\frac{a}{b}=\frac{c}{d}=k\)

\(\Rightarrow a=kb;c=kd\)

Ta xét :

\(\frac{a-b}{b}=\frac{kb-b}{b}=\frac{b\left(k-1\right)}{b}=k-1\)

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

Ta thấy \(k-1=k-1\)

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

\(\RightarrowĐPCM\)

Answer 2

Rất dễ:

Ta có: \(\frac{c}{d}=\frac{a}{b}\Rightarrow\frac{a}{b}-1=\frac{c}{d}-1\)

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

ĐPCM

Answer 3

Ta có

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

Answer 4

Ta có :\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{b}-1=\frac{c}{d}-1\Rightarrow\frac{a-b}{b}=\frac{c-d}{d}\)

\(\RightarrowĐPCM\)