Question

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

Chứng tỏ \(\dfrac{a+b}{b}=\dfrac{c+d}{d};\dfrac{a-b}{b}=\dfrac{c-d}{d}\)

Answer 1

a) Ta có : điều đề bài cho:\(\dfrac{a}{b}=\dfrac{c}{d}\)

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

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

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

b) Điều đề bài cho:

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

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

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

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