To find the missing part in the expression
\[ \frac{x^2 - 2}{x^2 - 5} - \frac{4x + 1}{5 - x^2} + \frac{?}{x^2 - 5}, \]
we first notice that \(5 - x^2\) can be rewritten as \(-(x^2 - 5)\). Thus, we can rewrite the second fraction:
\[ \frac{4x + 1}{5 - x^2} = \frac{4x + 1}{-(x^2 - 5)} = -\frac{4x + 1}{x^2 - 5}. \]
Now our expression looks like this:
\[ \frac{x^2 - 2}{x^2 - 5} + \frac{-(4x + 1)}{x^2 - 5} + \frac{?}{x^2 - 5}. \]
Combining these fractions gives:
\[ \frac{x^2 - 2 - (4x + 1) + ?}{x^2 - 5}. \]
Simplifying the numerator:
\[ x^2 - 2 - 4x - 1 + ? = x^2 - 4x - 3 + ?. \]
Now we have the final expression:
\[ \frac{x^2 - 4x - 3 + ?}{x^2 - 5}. \]
To find the missing part such that this expression equals zero (the result of the difference of the two original fractions), we set:
\[ x^2 - 4x - 3 + ? = 0. \]
This means we need to solve for ?:
\[ ? = - (x^2 - 4x - 3). \]
Thus, the missing part is:
\[ ? = -x^2 + 4x + 3. \]
Therefore, the final answer for the missing part is:
\[ \boxed{-x^2 + 4x + 3}. \]
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