$\left\{\begin{matrix}x=-\frac{uy}{u-y}\text{, }&u\neq 0\text{ and }\left(y=0\text{ or }y\neq u\right)\text{ and }\left(y=0\text{ or }|arg(\sqrt{\frac{y^{2}}{u^{2}}}u)-arg(y)|<\pi \right)\\x\neq -y\text{, }&u=-y\text{ and }y\neq 0\text{ and }|arg(-y)-arg(y)|<\pi \\x\neq 0\text{, }&y=0\text{ and }u=0\end{matrix}\right.$

$\left\{\begin{matrix}u=\frac{xy}{x+y}\text{, }&\left(y\geq 0\text{ and }y<-x\right)\text{ or }\left(y\geq 0\text{ and }x>0\right)\text{ or }\left(y\leq 0\text{ and }x<0\right)\text{ or }\left(y>-x\text{ and }y\leq 0\right)\\u\neq 0\text{, }&y=0\text{ and }x=0\end{matrix}\right.$

$\left\{\begin{matrix}x=-\frac{uy}{u-y}\text{, }&\left(yu\text{ and }y\leq 0\right)\text{ or }\left(y>u\text{ and }u>0\right)\\x\neq 0\text{, }&y=0\text{ and }u=0\end{matrix}\right.$