Let's simplify the given expression step by step:

$x^3 - \frac{1}{x^2} - 1 + \frac{1}{x^2} + x$

1. Combine like terms: $x^3 - 1 + x + \left( -\frac{1}{x^2} + \frac{1}{x^2} \right)$

2. The terms $-\frac{1}{x^2} + \frac{1}{x^2}$ cancel each other out. So, the expression simplifies to:

$x^3 + x - 1$

So, the simplified expression is:

$x^3 + x - 1$

Would you like further details or explanations on this? Feel free to ask.

Further questions to explore:

1. How do you factor cubic expressions like $x^3 + x - 1$?
2. How would you solve $x^3 + x - 1 = 0$?
3. What are some other ways to simplify rational expressions involving polynomials?
4. How can you handle more complex fractions or higher-order polynomials?
5. Can this expression be factored into simpler terms?

Tip: Always look for like terms to simplify expressions before attempting any further operations!