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To simplify the given expression, let's first find a common denominator for the fractions:
4/(x^2 + 2x + 1) - 1/(x^2 - 2x + 1) = -1/(x^2 - 1)
The common denominator is (x^2 + 2x + 1)(x^2 - 2x + 1)(x^2 - 1). Multiplying each term by the common denominator:
4(x^2 - 1) - (x^2 + 2x + 1) - (x^2 - 2x + 1) = -1
Expanding and simplifying:
4x^2 - 4 - x^2 - 2x - 1 - x^2 + 2x - 1 = -1
Combining like terms:
2x^2 - 4 = 0
Dividing both sides by 2:
x^2 - 2 = 0
Now we have the equation x^2 - 2 = 0.
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