$$\frac{4a+5b}{4a-5b}=\frac{4c+5d}{4c-5d}$$
$\left\{\begin{matrix}a=\frac{bc}{d}\text{, }&c\neq \frac{5d}{4}\text{ and }b\neq 0\text{ and }d\neq 0\\a\neq 0\text{, }&b=0\text{ and }d=0\text{ and }c\neq 0\end{matrix}\right.$
$\left\{\begin{matrix}b=\frac{ad}{c}\text{, }&c\neq \frac{5d}{4}\text{ and }a\neq 0\text{ and }c\neq 0\\b\neq 0\text{, }&a=0\text{ and }c=0\text{ and }d\neq 0\end{matrix}\right.$
