Answer
$\{x| x\ne\pm2 \}$
Work Step by Step
To find the domain of $h(x)=\dfrac{2x}{x^2-4}$, use the fact that the denominator should not be equal to zero. This means you have to solve $x^2-4=0$.
Factor the binomial:
$(x-2)(x+2)=0$
Use the Zero-Product Property by equating each factor to $0$, then solve each equation:
$\begin{align*}
x-2&=0 &\text{or}& &x+2=0\\
x&=2 &\text{or}& &x=-2
\end{align*}$
Therefore, the value of $x$ cannot be $-2$ or $2$.
