Cho tỉ lệ thức: 

- Hướng dẫn giải

Đặt $\frac{a}{b}=\frac{c}{d}=k(k\in R)\Rightarrow a=k.b;c=k.d$

Ta có: $$\begin{gathered} \frac{5a+3b}{3a-7b}=\frac{5kb+3b}{3kb-7b}=\frac{b\left(5k+3\right)}{b\left(3k-7\right)}=\frac{5k+3}{3k-7}\left(1\right) \\ \frac{5c+3d}{3c-7d}=\frac{5kd+3d}{3kd-7d}=\frac{d\left(5k+3\right)}{d\left(3k-7\right)}=\frac{5k+3}{3k-7}\left(2\right) \end{gathered}$$

Từ (1), (2) => đpcm