Question

dạng toán chứng minh tỉ lệ thức

bài 1 cho \(\frac{a}{b}=\frac{c}{d}\)

1,chứng minh \(\frac{a-2b}{b}=\frac{c-2d}{d}\)

 

Answer 1

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{2b}{2d}=\frac{a-2b}{c-2d}\)

\(\Rightarrow\frac{b}{d}=\frac{a-2b}{c-2d}\)

\(\Rightarrow\frac{a-2b}{b}=\frac{c-2d}{d}\)

Answer 2

Đặt \(\frac{a}{b}=\frac{c}{d}=K\)

\(\Rightarrow a=Kb\)và \(c=Kd\)

\(\frac{a-2b}{b}=\frac{Kb-2b}{b}=\frac{b\left(K-2\right)}{b}=K-2\)

\(\frac{c-2d}{d}=\frac{Kd-2d}{d}=\frac{d\left(K-2\right)}{d}=K-2\)

Vậy\(\frac{a-2b}{b}=\frac{c-2d}{d}\)