To simplify the expression $\frac{x^2 + 7x + 18}{x - 4}$, we need to examine if the numerator, $x^2 + 7x + 18$, can be factored in a way that allows us to cancel out a factor of $(x - 4)$.

Step 1: Check for Factorization of $x^2 + 7x + 18$

For factoring a quadratic expression $x^2 + bx + c$, we look for two numbers that multiply to $18$ (the constant term) and add up to $7$ (the coefficient of $x$).

1. Factors of $18$ are: $1 \times 18$, $2 \times 9$, and $3 \times 6$.
2. None of these factor pairs add up to $7$, so $x^2 + 7x + 18$ cannot be factored further over