The given image presents three functions: $f(x)$, $g(x)$, and $h(x)$, as well as a request to evaluate $\left( \frac{f}{h} \right)(1)$.

The functions are: $f(x) = -x^2 + x$ $g(x) = \frac{2}{x + 2}$ $h(x) = -2x - 1$

To find $\left( \frac{f}{h} \right)(1)$, we need to:

1. Calculate $f(1)$.
2. Calculate $h(1)$.
3. Compute $\frac{f(1)}{h(1)}$.

Step 1: Calculate $f(1)$

$f(1) = -(1)^2 + 1 = -1 + 1 = 0$

Step 2: Calculate $h(1)$

$h(1) = -2(1) - 1 = -2 - 1 = -3$

Step 3: Compute $\frac{f(1)}{h(1)}$

$\frac{f(1)}{h(1)} = \frac{0}{-3} = 0$

Thus, $\left( \frac{f}{h} \right)(1) = 0$.

Would you like more details or explanations? Here are some related questions you can explore:

1. How would the result change if we evaluated $\frac{f}{g}$(1)?
2. What is $f(x) + g(x)$ evaluated at $x = 1$?
3. Can you find the domain of $g(x)$?
4. How does the shape of $f(x)$ look graphically?
5. What happens to $\frac{f}{h}$(x) as $x \to \infty$?

Tip: When working with function divisions, always ensure that the denominator is non-zero to avoid undefined expressions.