Solve x^2-(a-3)x-3a/x^2-4geq0

$$\frac { x ^ { 2 } - ( a - 3 ) x - 3 a } { x ^ { 2 } - 4 } \geq 0$$

Solve for x

$$\left\{\begin{matrix}\\x\in \mathrm{R}\setminus ((\frac{-|a+3|+a-3}{2},\infty)\text{, }a=-3\cup (\frac{|a+3|+a-3}{2},\infty)\text{, }a\neq -3\cup (\frac{-|a+3|+a-3}{2},-2]\cup [2,\infty))\text{, }&\text{unconditionally}\\x=\frac{|a+3|+a-3}{2}\text{, }&|a|\neq 2\\x<-2\text{, }&a=-3\\x\in [\frac{|a+3|+a-3}{2},-2)\text{, }&a<-3\text{ or }(a\geq -3\text{ and }a<-2)\\x\geq \frac{|a+3|+a-3}{2}\text{, }&a>2\\x>2\text{, }&a\leq 2\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=x\text{, }&|x|\neq 2\\a\leq x\text{, }&x\geq -3\text{ and }|x|>2\\a\in \mathrm{R}\text{, }&x=-3\\a\geq x\text{, }&x\leq -3\text{ or }|x|<2\end{matrix}\right.$$