Ta có: \(\frac{a}{b}=\frac{c}{d}\) \(\Rightarrow\) ad = cb
Ta có: ab + cd = bc + cd
(a + c)d = (b + d)c
\(\Rightarrow\) a + \(\frac{c}{b}\) + d = \(\frac{c}{d}\)
Mà \(\frac{a}{b}=\frac{c}{d}\) \(\Rightarrow\) \(\frac{a}{b}\) = a + \(\frac{c}{b}\) + d