WAEC Further Mathematics 2022 Paper

Concept:This is a partial fractions problem where two fractions are combined and then the numerators are compared.Explanation:The denominator factors as $x^2-3x-4 = (x+1)(x-4)$.Combine the right-hand side over the common denominator $(x+1)(x-4)$.$$\frac{5}{x+1}+\frac{3}{x-4} = \frac{5(x-4)+3(x+1)}{(x+1)(x-4)}$$Simplify the numerator:$$5(x-4)+3(x+1) = 5x-20+3x+3 = 8x-17$$So the identity becomes:$$\frac{8x+m}{x^2-3x-4} \equiv \frac{8x-17}{x^2-3x-4}$$Since the denominators are equal, equate the numerators:$$8x+m \equiv 8x-17$$Therefore, $m = -17$.Answer:$m = -17$, so the correct option is C.