Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
A
\(\frac{2x}{(x - 2)(x + 2)(x^2 - 4)}\)
B
\(\frac{2x}{x^2 - 4}\)
C
\(\frac{x}{x^2 - 4}\)
D
\(\frac{4x}{x^2 - 4}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
= \(\frac{(x + 2) + (x - 2) + 2x}{(x + 2)(x - 2)}\)
= \(\frac{4x}{x^2 - 4}\)
Source: Myschool Past Questions Archive (Record #32113)