Question

cho tỉ lệ thức a/b=c/d chứng minh 4a-3b/a=4c-3d/c
help me

Answer 1

Có \(\frac{a}{b}=\frac{c}{d}\Rightarrow a=bk;c=dk\)

\(\Rightarrow\frac{4a-3b}{a}=\frac{4bk-3b}{bk}=\frac{b\left(4k-3\right)}{bk}=\frac{4k-3}{k}\left(1\right)\)

\(\Rightarrow\frac{4c-3d}{c}=\frac{4dk-3d}{dk}=\frac{d\left(4k-3\right)}{dk}=\frac{4k-3}{k}\left(2\right)\)

Từ \(\left(1\right)\left(2\right)\Rightarrow\frac{4a-3b}{a}=\frac{4c-3d}{c}\left(đpcm\right)\)