To find $(h - f)(x)$, we need to subtract $f(x)$ from $h(x)$.

Given functions: $f(x) = x^2 + 5x + 6$ $h(x) = x + 2$

Now, calculate $(h - f)(x)$: $(h - f)(x) = h(x) - f(x)$

Substituting the values of $h(x)$ and $f(x)$: $(h - f)(x) = (x + 2) - (x^2 + 5x + 6)$

Simplify by distributing the negative sign: $(h - f)(x) = x + 2 - x^2 - 5x - 6$

Combine like terms: $(h - f)(x) = -x^2 - 4x - 4$

So, $(h - f)(x) = -x^2 - 4x - 4$.

Would you like to see details or have any questions? Here are some related questions:

1. How do you find $(f + h)(x)$ for the given functions?
2. What is $(f \times h)(x)$?
3. Can you find the domain of the function $(h - f)(x)$?
4. How do you find $(h \div f)(x)$ and simplify it?
5. What are the roots of $(h - f)(x) = 0$?

Tip: When combining functions, carefully distribute any negative signs and combine like terms correctly to avoid errors.