JAMB 1986 · UME · Q26

Simplify $\dfrac{1}{x - 2} + \dfrac{1}{x + 2} + \dfrac{2x}{x^2 - 4}$ .

Worked solution (try it first)

Since $x^2 - 4 = (x - 2)(x + 2)$ , the LCD is just $x^2 - 4$ .
Change each top to match: $\frac{1}{x - 2} = \frac{x + 2}{x^2 - 4}$ and $\frac{1}{x + 2} = \frac{x - 2}{x^2 - 4}$ .
Add the tops: $(x + 2) + (x - 2) + 2x = 4x$ .
So the sum is $\dfrac{4x}{x^2 - 4}$ , option D.