The expression in the image is:

$\frac{11 + x}{x^3} + 2x(5 - x)$

To simplify and work through this, let’s break it into parts:

1. The first term is $\frac{11 + x}{x^3}$, which involves a polynomial divided by a cubic power of $x$.
2. The second term is $2x(5 - x)$, which can be expanded.

Let me simplify the second term first:

$2x(5 - x) = 2x \cdot 5 - 2x \cdot x = 10x - 2x^2$

Now, putting everything together, we have:

$\frac{11 + x}{x^3} + 10x - 2x^2$

This is the simplified form of the expression. Would you like to proceed with solving for $x$ or further analysis of this equation? Let me know!

Here are some related questions you could explore next:

1. How do you solve rational expressions like $\frac{11 + x}{x^3} = 0$?
2. What is the process for simplifying rational functions?
3. How can we solve for $x$ in a cubic equation?
4. How do we graph rational functions?
5. What happens when we apply limits to rational expressions?

Tip: Always check for restrictions in rational functions. In this case, $x \neq 0$ because of the $x^3$ in the denominator.