Question

Cho phân số \(\dfrac{a}{b}\) . Chứng minh rằng : 

Nếu \(\dfrac{a-x}{b-y}=\dfrac{a}{b}\) thì \(\dfrac{x}{y}=\dfrac{a}{b}\) 

Answer 1

\(\dfrac{a-x}{b-y}=\dfrac{a}{b}\)

\(\Rightarrow\dfrac{a-x}{a}=\dfrac{b-y}{b}\)

\(\Rightarrow1-\dfrac{x}{a}=1-\dfrac{y}{b}\)

\(\Rightarrow\dfrac{x}{a}=\dfrac{y}{b}\)

\(\Rightarrow\dfrac{x}{y}=\dfrac{a}{b}\)