Question

Cho tỉ lệ thức a/b = c/d. Chứng yor rằng: a/a+b = c/c+d

Answer 1

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

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

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

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

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

Answer 2

Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\)

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

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

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

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