To solve the expression:

$x + \frac{4}{x} - \frac{3}{x} - \frac{3}{x + 2}$

We will simplify it step by step:

1. Combine the terms with the same denominator, which are $\frac{4}{x}$ and $\frac{3}{x}$:

$x + \left(\frac{4}{x} - \frac{3}{x}\right) - \frac{3}{x + 2}$

This simplifies to:

$x + \frac{4 - 3}{x} - \frac{3}{x + 2} = x + \frac{1}{x} - \frac{3}{x + 2}$

2. So, the simplified expression is:

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

This is as simplified as we can get without knowing the value of $x$.

---

Would you like to evaluate this expression for a specific value of $x$ or need further details?

Here are 5 questions related to this:

1. Would you like to solve for specific values of $x$?
2. Should we explore finding a common denominator?
3. Would you like to see how this can be plotted?
4. Are you interested in further simplifying this in case of any constraints on $x$?
5. How do you think this expression behaves as $x$ approaches infinity?

Tip: When simplifying, always check for terms with the same denominator to combine them effectively.