21. $y=\frac{3}{x^{2}-4}$.
Solution. By setting the denominator to zero, we solve the obtained equation: $x^{2}-4=0 ;(x+2)(x-2)=0 ; x_{1}=-2, x_{2}=2$. Therefore, the denominator equals zero at the values $x=-2$ and $x=2$, which cannot belong to the domain of the given function. Excluding them, we obtain three intervals ( $-\infty,-2$ ), $(-2,2)$, and ( $2, \infty$ ), which serve as the domain of the given function.