\(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\\ \Rightarrow\dfrac{5a+3b}{5c+3d}=\dfrac{5a-3b}{5c-3d}=\dfrac{5a+3b+5a-3b}{5c+3d+5c-3d}=\dfrac{5a+3b-5a+3b}{5c+3d-5c+3d}=\dfrac{10a}{10c}=\dfrac{6b}{6d}=\dfrac{a}{c}=\dfrac{b}{d}\\ \Rightarrow ad=bc;\dfrac{a}{b}=\dfrac{c}{d}\)
