Sửa đề : Cho \(\frac{a}{b}=\frac{c}{d}\).Chứng minh : \(a,\frac{a}{3a+b}=\frac{c}{3c+d}\)
b, \(\frac{a^2-b^2}{c^2-d^2}=\frac{ab}{cd}\)
Bài làm:
\(a,\)Ta có : \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)
\(\Rightarrow\frac{a}{c}=\frac{3a}{3c}=\frac{b}{d}=\frac{3a+b}{3c+d}\Rightarrow\frac{a}{3a+b}=\frac{c}{3c+d}\)
\(b,\)Ta có : \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{ab}{cd}=\frac{a}{c}\cdot\frac{a}{c}=\frac{b}{d}\cdot\frac{b}{d}=\frac{a^2-b^2}{c^2-d^2}\)