JAMB 1988 · UME · Q23

Simplify $\dfrac{1}{x^2 + 5x + 6} + \dfrac{1}{x^2 + 3x + 2}$ .

Worked solution (try it first)

Factorise the bottoms: $x^2 + 5x + 6 = (x + 2)(x + 3)$ and $x^2 + 3x + 2 = (x + 1)(x + 2)$ .
The common denominator is $(x + 1)(x + 2)(x + 3)$ .
Each top is multiplied by the factor its bottom lacks, so the top is $(x + 1) + (x + 3) = 2x + 4$ .
Factorise the top as $2(x + 2)$ and cancel $x + 2$ .
This leaves $\dfrac{2}{(x + 1)(x + 3)}$ , option C.