Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). CMR:

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

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

\(\dfrac{a+b}{a}=\dfrac{bk+b}{bk}=\dfrac{k+1}{k}\)

\(\dfrac{c+d}{c}=\dfrac{dk+d}{d}=\dfrac{k+1}{k}\)

=>(a+b)/a=(c+d)/c

Answer 2

Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\)

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

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

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

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