Answer
$\{-2,-1\}$
Work Step by Step
$1+\frac{3}{x}=\frac{-2}{x^2}$
Rearranging:
$\frac{x+3}{x}=\frac{-2}{x^2}$
Multiplying both sides by $x^2$:
$x^2+3x=-2,$
$x^2+3x+2=0,$
$x^2+x+2x+2=0,$
$x(x+1)+2(x+1)=0,$
$(x+2)(x+1)=0,$
Thus, $x=-2$ or $x=-1$
Check:
For $x=-2, 1-\frac{3}{2}=\frac{-2}{4}, \frac{2-3}{2}=\frac{-1}{2}, -\frac{1}{2}=-\frac{1}{2}$
For $x=-1, 1-3=-2, -2=-2$
