Limiting points of elementary set

Question

I consider the following set

$$A:=\left\{ \frac{3mn}{2(m^2+mn+n^2)}; m,n \in \mathbb Z; \text{ and }m,n \text{ are not both zero}\right\}$$

Is it possible to identify the closure of $A$ in the reals?

Answer 1

Set $x=n/m$, rational dense in the reals, so the closure of $A$ is the image of the function $f(x)=3x/(2(x^2+x+1))$, so the interval $[-3/2,1/2]$.