Question

cho \(\dfrac{a}{b}\) =\(\dfrac{c}{d}\)   cm rằng 

a) \(\dfrac{a}{a-b}\) =\(\dfrac{c}{c-d}\)   b)\(\dfrac{a}{b}\) =\(\dfrac{a+c}{b+d}\)   c) \(\dfrac{a}{3a+d}\) =\(\dfrac{c}{3c+d}\)   d)\(\dfrac{a.c}{b.d}\) =\(\dfrac{a^2+c^2}{b^2+c^2}\)   e)\(\dfrac{a.b}{c.d}\) =\(\dfrac{a^2-b^2}{c^2-d^2}\)   f)\(\dfrac{a.b}{c.d}\) =\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\) 

mn giúp mk vs ạ! thanks

Answer 1

a) Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\)

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

\(\Leftrightarrow\dfrac{b}{a}-1=\dfrac{d}{c}-1\)

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

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

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