Find the domain of the rational function \( R(x)=\frac{x+3}{x-4} \). \( (-\infty,-3] \cup(4, \infty) \) \( (-3,4) \) \( (4, \infty) \) \( (-\infty, 4) \cup(4, \infty) \)

To find the domain of the rational function \( R(x) = \frac{x+3}{x-4} \), we need to identify the values of \( x \) for which the function is defined. A rational function is undefined when its denominator is equal to zero. 1. **Identify the denominator**: The denominator of \( R(x) \) is \( x - 4 \). 2. **Set the denominator to zero**: \[ x - 4 = 0 \] Solving this gives: \[ x = 4 \] 3. **Determine the domain**: The function \( R(x) \) is undefined at \( x = 4 \). Therefore, the domain includes all real numbers except \( x = 4 \). 4. **Express the domain in interval notation**: The domain can be expressed as: \[ (-\infty, 4) \cup (4, \infty) \] Thus, the correct answer is \( (-\infty, 4) \cup (4, \infty) \).