Question

cho \(\dfrac{a}{b}=\dfrac{c}{d}\left(a,b,c,d\ne0\right)\) chung minh rang

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

b ,\(\dfrac{2a+5b}{3a-4d}=\dfrac{2c+5d}{3c-4d}\)

giup minh nhe minh dang can gap

Answer 1

Answer 2

a. Ta có : ( a + b )( c - d ) = ac-ad+bc-bd (1)

( a - b )( c + d ) = ac+ad-bc+bd (2)

Từ giả thuyết : \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow ad=bc\) (3)

Từ (1) , ( 2) và ( 3) \(\Rightarrow\)( a + b )( c - d) = ( a - b)( c + d )

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