Find the domain of the following rational function. \[ R(x)=\frac{x}{x^{3}+8} \]

To find the domain of the rational function \( R(x) = \frac{x}{x^3 + 8} \), we need to identify the values of \( x \) that make the denominator zero, as these values are excluded from the domain. Start by setting the denominator equal to zero: \[ x^3 + 8 = 0 \] This can be rewritten as: \[ x^3 = -8 \] Taking the cube root of both sides, we find: \[ x = -2 \] Thus, the function is undefined at \( x = -2 \). Therefore, the domain of \( R(x) \) includes all real numbers except \( -2 \). In interval notation, the domain is: \[ (-\infty, -2) \cup (-2, \infty) \]