Question

. Cho a/b = c/d với a, b, c, d > 0. Chứng minh rằng \(\dfrac{2a-3b}{2a+3b}=\dfrac{2c-3d}{2c+3d}\)

Answer 1

\(\dfrac{2a-3b}{2a+3b}=\dfrac{2c-3d}{2c+3d}\Rightarrow\dfrac{2a-3d}{2c-3d}=\dfrac{2a+3b}{2c-3d}\)

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

Answer 2

vì a/b = c/d

theo dãy tỉ số bằng nhau ta có

a/b =c/d = a+c/b+d = a-c/b-d (đỗi vị trí)

⇒  2a-2b/2a+3b = 2c-3d/2c-3d