Question

cho \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\). Chứng minh rằng

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

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

Answer 1

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