NECO 2023 · Paper 1 · Q12

Resolve $\dfrac{2x + 5}{(x + 3)(x + 2)}$ into partial fractions.

Worked solution (try it first)

Write $\dfrac{2x + 5}{(x + 3)(x + 2)} = \dfrac{A}{x + 3} + \dfrac{B}{x + 2}$ and multiply through by the bottom: $2x + 5 = A(x + 2) + B(x + 3)$ .
Put $x = -3$ , which makes $x + 3$ zero: $-1 = A(-1)$ , so $A = 1$ .
Put $x = -2$ , which makes $x + 2$ zero: $1 = B(1)$ , so $B = 1$ .
So the fraction is $\dfrac{1}{x + 3} + \dfrac{1}{x + 2}$ , option C.