Ta có ; \(\frac{a}{b}=\frac{c}{d}\)
\(\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{5a}{5c}=\frac{3b}{3d}=\frac{5a+3b}{5c+3d}\left(1\right)\)
Mặt khác ; \(\frac{a}{c}=\frac{b}{d}=\frac{5a}{5c}=\frac{3b}{3d}=\frac{5a-3b}{5c-3d}\left(2\right)\)
Từ : (1) và (2) => \(\frac{5a+3b}{5c+3d}=\frac{5a-3b}{5c-3d}\)
Suy ra ; \(\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}\) (đpcm)