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The given equation is:

\[
\frac{a+1}{(a+b)^2}x + \frac{a+1}{(a-b)^2} = \frac{a+1}{a^2 - b^2} + \frac{a+1}{(a-b)^2}x
\]

### Steps to Solve:

1. **Simplify \(a^2 - b^2\):**
   \[
   a^2 - b^2 = (a+b)(a-b)
   \]
   Thus, the equation becomes:
   \[
   \frac{a+1}{(a+b)^2}x + \frac{a+1}{(a-b)^2} = \frac{a+1}{(a+b)(a-b)} + \frac{a+1}{(a-b)^2}x
   \]

2. **Subtract \( \frac{a+1}{(a-b)^2}x \) from both sides:**
   \[
   \frac{a+1}{(a+b)^2}x = \frac{a+1}{(a+b)(a-b)}
   \]

3. **Cancel out the common factor \(a+1\):**
   (assuming \(a \neq -1\) to avoid division by zero)
   \[
   \frac{x}{(a+b)^2} = \frac

Solve the equation: \frac{a+1}{(a+b)^2}x + \frac{a+1}{(a-b)^2} = \frac{a+1}{a^2 - b^2} + \frac{a+1}{(a-b)^2}x

Learn how to solve a rational equation with variables a and b involving the difference of squares. This problem highlights key algebraic techniques, including factoring and simplifying expressions, suitable for students in Grades 9-12.

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