\(a,\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\)
\(\Rightarrow\frac{a}{c}+1=\frac{b}{d}+1\)
\(\Rightarrow\frac{a}{c}+\frac{c}{c}=\frac{b}{d}+\frac{d}{d}\)
\(\Rightarrow\frac{a+c}{c}=\frac{b+d}{d}\)
Ta có :
\(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\)
\(\Leftrightarrow\frac{3a}{3c}=\frac{5b}{5d}=\frac{3a+5b}{3c+5d}=\frac{3a-5b}{3c-5d}\)
\(\Rightarrow\frac{3a+5b}{3a-5b}=\frac{3a+5d}{3c-5d}\)