JAMB 1995 · UME · Q19

Express $\dfrac{5x - 12}{(x - 2)(x - 3)}$ in partial fractions.

Worked solution (try it first)

Write $\frac{5x - 12}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}$ , so $5x - 12 = A(x - 3) + B(x - 2)$ .
Put $x = 2$ : $-2 = -A$ , so $A = 2$ .
Put $x = 3$ : $3 = B$ .
So the partial fractions are $\frac{2}{x - 2} + \frac{3}{x - 3}$ , option B.