Question

2) Cho tỉ lệ thức $\frac{a}{b}=\frac{c}{d}$. Chứng minh: $\frac{2a-6b}{2b}=\frac{2c-6d}{2d}$

 

Answer 1

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=>a=bk; c=dk

\(\dfrac{2a-6b}{2b}=\dfrac{2\cdot bk-6b}{2b}=\dfrac{2b\left(k-3\right)}{2b}=k-3\)

\(\dfrac{2c-6d}{2d}=\dfrac{2\cdot dk-6d}{2d}=\dfrac{2d\left(k-3\right)}{2d}=k-3\)

Do đó: \(\dfrac{2a-6b}{2b}=\dfrac{2c-6d}{2d}\)

Answer 2

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow a=bk;c=dk\)

Thay \(a=bk;c=dk\) vào\(\dfrac{2a-6b}{2b}=\dfrac{2c-6d}{2d}\) ta được:

\(\dfrac{2a-6b}{2b}=\dfrac{2c-6d}{2d}=\dfrac{2bk-6b}{2b}=\dfrac{2dk-6d}{2d}=k-3\)

Vậy \(\dfrac{2a-6b}{2b}=\dfrac{2c-6d}{2d}\)