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 \(x\).

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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.

This guide walks through the simplification of a rational expression: x + 4/x - 3/x - 3/(x + 2). It covers combining like terms with the same denominator and simplifying rational expressions, suitable for Grades 8-10 students learning algebra.

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