\( ( x ) = x + 3 \quad g ( x ) = \frac { x ^ { 2 } + 5 x + 6 } { x + 2 } \)

It looks like you've provided two functions, \( f(x) \) and \( g(x) \). However, the function \( f(x) \) seems to be incomplete. I will assume you meant to write: \[ f(x) = x + 3 \] and \[ g(x) = \frac{x^2 + 5x + 6}{x + 2} \] Let's simplify \( g(x) \): 1. Factor the numerator \( x^2 + 5x + 6 \): \[ x^2 + 5x + 6 = (x + 2)(x + 3) \] 2. Substitute this back into \( g(x) \): \[ g(x) = \frac{(x + 2)(x + 3)}{x + 2} \] 3. For \( x \neq -2 \), we can simplify: \[ g(x) = x + 3 \] Thus, for \( x \neq -2 \), we have: \[ g(x) = x + 3 \] Now, we can see that both functions \( f(x) \) and \( g(x) \) are equal for all \( x \) except \( x = -2 \): \[ f(x) = g(x) \quad \text{for } x \neq -2 \] If you have any specific questions or further operations you'd like to perform with these functions, please let me know!