Given the functions \(f(x) = \sqrt{x+2}\) and \(g(x) = \frac{1}{x-3}\), find the domain of the sum of the functions \(f(x) + g(x)\).

Step 1 ：Step 1: Find the domain of each function separately.

Step 2 ：For \(f(x) = \sqrt{x+2}\), the domain is \(x \geq -2\) because the expression under the square root must be greater than or equal to 0.

Step 3 ：For \(g(x) = \frac{1}{x-3}\), the domain is \(x \neq 3\) because the denominator of a fraction cannot be 0.

Step 4 ：Step 2: Combine the two domains.

Step 5 ：The combined domain is the intersection of the two separate domains, which is \(x \geq -2\) and \(x \neq 3\).