Question

cho tỉ lệ thức a/b=c/d cmr: 5a+3b/2a-b=5c+3d/2c-d

help me plese!

Answer 1

Theo đề bài, ta có : \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{5a}{3b}=\dfrac{5c}{3d}\)

\(\Leftrightarrow\dfrac{5a}{5c}=\dfrac{3b}{3d}=\dfrac{5a+3b}{5c+3d}\)

\(\Rightarrow\dfrac{a}{c}=\dfrac{5a+3b}{5c+3d}\) (1)

Lại có : \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{2a}{b}=\dfrac{2c}{d}\)

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

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

Từ (1) và (2) : \(\Rightarrow\dfrac{5a+3b}{5c+3d}=\dfrac{2a-b}{2c-d}\Leftrightarrow\dfrac{5a+3b}{2a-b}=\dfrac{5c+3d}{2c-d}\left(đpcm\right)\)