$$f(AY)=-\frac{2x^{2}+3x+9}{2(ax+1)}$$
$A=-\frac{2x^{2}+3x+9}{2Yf\left(ax+1\right)}$
$\left(a=0\text{ or }x\neq -\frac{1}{a}\right)\text{ and }Y\neq 0\text{ and }f\neq 0$
$Y=-\frac{2x^{2}+3x+9}{2Af\left(ax+1\right)}$
$\left(a=0\text{ or }x\neq -\frac{1}{a}\right)\text{ and }A\neq 0\text{ and }f\neq 0$
