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Subtract the following rational expressions and write the difference in simplest form if possible.
A
B
C
D
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1
Identify the given rational expressions: \(\frac{x+2}{x^2 - 4} - \frac{1}{x - 2}\).
Factor the denominator \(x^2 - 4\) as a difference of squares: \(x^2 - 4 = (x - 2)(x + 2)\).
Rewrite the first fraction with the factored denominator: \(\frac{x+2}{(x - 2)(x + 2)}\).
Express the second fraction with the common denominator \((x - 2)(x + 2)\) by multiplying numerator and denominator by \((x + 2)\): \(\frac{1}{x - 2} = \frac{x + 2}{(x - 2)(x + 2)}\).
Subtract the numerators over the common denominator: \(\frac{x + 2}{(x - 2)(x + 2)} - \frac{x + 2}{(x - 2)(x + 2)} = \frac{(x + 2) - (x + 2)}{(x - 2)(x + 2)}\).