Find the domain of the function. \( g(x)=\frac{3 x}{x^{2}-4} \) The domain is \( \square \). (Type your answer in interval notation.)

To find the domain of the function \( g(x)=\frac{3 x}{x^{2}-4} \), we need to determine where the function is defined. The denominator \( x^2 - 4 \) cannot be zero, as division by zero is undefined. Setting the denominator to zero gives us the equation \( x^2 - 4 = 0 \), which factors to \( (x - 2)(x + 2) = 0 \). This yields the values \( x = 2 \) and \( x = -2 \). Thus, the function is undefined at these points. The domain is all real numbers except \( x = 2 \) and \( x = -2\). In interval notation, we express this as \( (-\infty, -2) \cup (-2, 2) \cup (2, \infty) \). So the domain is \( (-\infty, -2) \cup (-2, 2) \cup (2, \infty) \).