JAMB 1998 · UME · Q16

Expressions, formulae & change of subject

Express $\dfrac{11x + 2}{6x^2 - x - 1}$ in partial fractions.

Worked solution (try it first)

Factorise the bottom: $6x^2 - x - 1 = (3x + 1)(2x - 1)$ .
Write $11x + 2 = A(2x - 1) + B(3x + 1)$ .
Put $x = -\frac13$ : $-\frac53 = -\frac53A$ , so $A = 1$ .
Put $x = \frac12$ : $\frac{15}{2} = \frac52B$ , so $B = 3$ .
So the answer is $\frac{1}{3x + 1} + \frac{3}{2x - 1}$ , option D.

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