Solve x+a/y+a+y/x>2

$$\frac { x + a } { y + a } + \frac { y } { x } > 2$$

Solve for x

$$\left\{\begin{matrix}x\in \left(y,0\right)\text{, }&\left(y<0\text{ and }a<0\right)\text{ or }\left(a>-y\text{ and }y<0\right)\\x\in \left(0,y\right)\text{, }&\left(y>0\text{ and }a<-y\right)\text{ or }\left(y>0\text{ and }a>0\right)\\x\in \left(0,y+a\right)\text{, }&a>-y\text{ and }a\leq 0\\x<y\text{, }&a>0\text{ and }a<-y\\x<y+a\text{, }&a\leq 0\text{ and }a<-y\\x>y\text{, }&a>-y\text{ and }a<0\\x>y+a\text{, }&a\geq 0\text{ and }a>-y\\x\in \left(y+a,0\right)\text{, }&a\geq 0\text{ and }a<-y\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y\in \left(-a,x\right)\text{, }&\left(x>-a\text{ and }x<0\right)\text{ or }\left(x>-a\text{ and }a<0\right)\\y\in \left(-a,x-a\right)\text{, }&x>0\text{ and }a\geq 0\\y>x\text{, }&a>0\text{ and }x>0\\y>x-a\text{, }&x>0\text{ and }a\leq 0\\y\in \left(x,-a\right)\text{, }&\left(x>0\text{ and }x<-a\right)\text{ or }\left(a>0\text{ and }x<-a\right)\\y\in \left(x-a,-a\right)\text{, }&x<0\text{ and }a\leq 0\\y<x\text{, }&a<0\text{ and }x<0\\y<x-a\text{, }&a\geq 0\text{ and }x<0\end{matrix}\right.$$