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The partial fraction decomposition given here is:

\[
\frac{16x + 34}{(2x + 2)(2x + 4)} = \frac{A}{2x + 2} + \frac{B}{2x + \, \square}
\]

Looking at the denominator, \((2x + 2)(2x + 4)\), we see that the missing term in the denominator of the second fraction is \(2x + 4\). 

So, the correct form for the partial fraction decomposition would be:

\[
\frac{16x + 34}{(2x + 2)(2x + 4)} = \frac{A}{2x + 2} + \frac{B}{2x + 4}
\]

To proceed with solving for \(A\) and \(B\), you would:

1. Multiply both sides by the denominator \((2x + 2)(2x + 4)\) to eliminate the fractions.
2. Set up an equation by expanding and then matching coefficients of \(x\) terms.

Would you like a detailed solution for finding \(A\) and \(B\)?

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Here are some related questions to deepen understanding:
1. What is partial fraction decomposition and when is it used?
2. How do you handle partial fraction decomposition when factors are repeated?
3. How do you determine the form of the decomposition if the denominator has a quadratic factor?
4. Why is it necessary to match coefficients to find \(A\) and \(B\)?
5. How would the approach change if the numerator had a higher degree than the denominator?

**Tip:** For partial fraction decomposition, always check if the degree of the numerator is lower than the denominator; if not, perform polynomial division first.

Perform partial fraction decomposition for \(\frac{16x + 34}{(2x + 2)(2x + 4)}\).

Learn how to perform partial fraction decomposition for the expression \(\frac{16x + 34}{(2x + 2)(2x + 4)}\). This solution breaks down the steps to identify the correct form of partial fractions and solve for constants.

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