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The provided problem asks for the indicated operations on the following three expressions:

\[
x + \frac{4}{x^2 - 16} - \frac{x^2}{x + 4}
\]

We are required to simplify this expression and express the answer in the form \(\frac{A}{B}\).

Let's begin solving this.

### Step 1: Factor the denominator of the second expression.
The denominator \(x^2 - 16\) is a difference of squares:
\[
x^2 - 16 = (x - 4)(x + 4)
\]
Thus, the second term becomes:
\[
\frac{4}{(x - 4)(x + 4)}
\]

### Step 2: Simplify the third expression.
The third term is \(\frac{x^2}{x + 4}\). We leave this as is for now.

### Step 3: Combine all terms under a common denominator.
To combine the expressions, we need a common denominator. The common denominator will be \((x - 4)(x + 4)\).

Let's rewrite the terms with this common denominator:

- The first term \(x\) can be written as \(\frac{x(x - 4)(x + 4)}{(x - 4)(x + 4)} = \frac{x(x^2 - 16)}{(x - 4)(x + 4)}\).
- The second term is already in the desired form: \(\frac{4}{(x - 4)(x + 4)}\).
- The third term \(\frac{x^2}{x + 4}\) can be rewritten as \(\frac{x^2(x - 4)}{(x - 4)(x + 4)}\).

Now, let's combine the terms and simplify.The simplified expression is:

\[
\frac{4(x^2 - 4x + 1)}{x^2 - 16}
\]

This is in the form \(\frac{A}{B}\), where:

\[
A = 4(x^2 - 4x + 1)
\]
and
\[
B = x^2 - 16
\]

Thus:

\[
A = 4(x^2 - 4x + 1) = 4x^2 - 16x + 4
\]
\[
B = (x - 4)(x + 4)
\]

### Final Answer:
- \(A = 4x^2 - 16x + 4\)
- \(B = x^2 - 16\)

Would you like more details on any of the steps? Here are five related questions for further exploration:

1. How do you factor a quadratic expression like \(x^2 - 16\)?
2. What are the steps to combine fractions with different denominators?
3. How can you apply the difference of squares to simplify expressions?
4. Why is it important to find a common denominator when adding or subtracting fractions?
5. How do you expand and simplify polynomials like \(4(x^2 - 4x + 1)\)?

**Tip**: Always check if the final expression can be factored further to simplify it even more.

Perform the indicated operations on the three expressions: x + 4/(x^2 - 16) - x^2/(x + 4). Express your answer in the form A/B.

Learn how to simplify the expression x + 4/(x^2 - 16) - x^2/(x + 4) using algebraic techniques like factoring and finding a common denominator. This step-by-step guide is suitable for students in Grades 9-12, focusing on rational expressions and the difference of squares formula.

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