JAMB Mathematics 2015 Paper

Concept:Adding two algebraic fractions requires factoring the denominators and then combining over the least common multiple (LCM).Explanation:Factor each denominator first.$x^2 + 3x + 2 = (x+1)(x+2)$$x^2 + 5x + 6 = (x+2)(x+3)$So the expression becomes:$$\frac{1}{(x+1)(x+2)} + \frac{1}{(x+2)(x+3)}$$The LCM of the denominators is $(x+1)(x+2)(x+3)$.Rewrite each fraction with this common denominator:$$\frac{x+3}{(x+1)(x+2)(x+3)} + \frac{x+1}{(x+1)(x+2)(x+3)}$$Add the numerators:$$\frac{(x+3)+(x+1)}{(x+1)(x+2)(x+3)} = \frac{2x+4}{(x+1)(x+2)(x+3)}$$Factor the numerator:$$\frac{2(x+2)}{(x+1)(x+2)(x+3)}$$Cancel the common factor $(x+2)$:$$\frac{2}{(x+1)(x+3)}$$Answer:$\frac{2}{(x+1)(x+3)}$Correct option: D.