$\left\{\begin{matrix}a=\frac{2x+3}{fgx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }f\neq 0\\a\in \mathrm{C}\text{, }&\left(g=0\text{ or }f=0\right)\text{ and }x=-\frac{3}{2}\end{matrix}\right.$

$\left\{\begin{matrix}f=\frac{2x+3}{agx}\text{, }&x\neq 0\text{ and }a\neq 0\text{ and }g\neq 0\\f\in \mathrm{C}\text{, }&\left(a=0\text{ or }g=0\right)\text{ and }x=-\frac{3}{2}\end{matrix}\right.$

$\left\{\begin{matrix}a=\frac{2x+3}{fgx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }f\neq 0\\a\in \mathrm{R}\text{, }&\left(g=0\text{ or }f=0\right)\text{ and }x=-\frac{3}{2}\end{matrix}\right.$

$\left\{\begin{matrix}f=\frac{2x+3}{agx}\text{, }&x\neq 0\text{ and }a\neq 0\text{ and }g\neq 0\\f\in \mathrm{R}\text{, }&\left(a=0\text{ or }g=0\right)\text{ and }x=-\frac{3}{2}\end{matrix}\right.$