The expression you provided is:

$x - \frac{8}{\sqrt{x+2}}$

To simplify this expression further:

• The term $\frac{8}{\sqrt{x+2}}$ is already in its simplest form.
• There is no factorization or common terms between $x$ and $\frac{8}{\sqrt{x+2}}$.

Thus, the expression cannot be simplified any further algebraically. You may rewrite it in different formats, but it won't reduce to a simpler form.

If you were considering other types of manipulations, like rationalizing the denominator or considering specific values of $x$, that could lead to further steps, but the current form is already simplified.

Would you like more details or have any questions on this?

Here are 5 related questions you could explore:

1. How can you rationalize the denominator of a fraction involving a square root?
2. What are the restrictions on $x$ for the given expression $x - \frac{8}{\sqrt{x+2}}$?
3. Can this expression be simplified further if specific values for $x$ are substituted?
4. How do you simplify expressions involving variables under a square root?
5. How does the derivative of $x - \frac{8}{\sqrt{x+2}}$ look?

Tip: To simplify expressions with square roots in the denominator, rationalizing may help, but it's not always necessary if the expression is already simplified.