Question

Bài 1 : Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng Minh :

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

b) \(\dfrac{a^2}{b^2}=\dfrac{ac+c^2}{bd+d^2}\)

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

d) \(\dfrac{2a-3c}{2b-3d}=\dfrac{a}{b}\)

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

Answer 1

\(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow ad=bc\)

Ta có:

Nếu:

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

\(\Leftrightarrow2a\left(b-d\right)+c\left(b-d\right)=a\left(2b+d\right)-c\left(2b+d\right)\)

\(\Leftrightarrow2ab-2ad+bc-cd=2ab+ad-2bc+cd\)

\(\Leftrightarrow ad=bc\)

\(\Leftrightarrow\dfrac{2a+c}{2b+d}=\dfrac{a-c}{b-d}\left(đpcm\right)\)