Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
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Correct Answer: Option D
Explanation:
\(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
= \(\frac{(x + 2) + (x - 2) + 2x}{(x + 2)(x - 2)}\)
= \(\frac{4x}{x^2 - 4}\)
\(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
= \(\frac{(x + 2) + (x - 2) + 2x}{(x + 2)(x - 2)}\)
= \(\frac{4x}{x^2 - 4}\)