Question

Chứng minh rằng \(\dfrac{a}{b}\) = \(\dfrac{c}{d}\) nếu:
a, \(\dfrac{a}{c}\) = \(\dfrac{a+b}{c+d}\)
b, \(\dfrac{b}{d}\) = \(\dfrac{a-b}{c-d}\)

Answer 1

a) \(\dfrac{a}{c}=\dfrac{a+b}{c+d}\)

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

=> ac + ad = ac + bc

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

b) \(\dfrac{b}{d}=\dfrac{a-b}{c-d}\)

=> b(c - d) = d(a - b)

=> bc - bd = ad - bd

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