WAEC Mathematics 2014 Paper

Concept:To compare two algebraic fractions, rewrite them with a common denominator and equate the numerators.Explanation:Start with the given equation:$$\frac{2}{x-3} - \frac{3}{x-2} = \frac{p}{(x-3)(x-2)}$$Combine the fractions on the left using the common denominator $(x-3)(x-2)$:$$\frac{2(x-2) - 3(x-3)}{(x-3)(x-2)} = \frac{p}{(x-3)(x-2)}$$Expand the numerator:$2(x-2) = 2x - 4$$-3(x-3) = -3x + 9$Now the numerator becomes:$$(2x - 4) + (-3x + 9) = -x + 5$$So the left side simplifies to:$$\frac{-x + 5}{(x-3)(x-2)}$$Since the denominators are equal, the numerators must be equal:$$p = -x + 5$$This is the same as:$$p = 5 - x$$Answer:$p = 5 - x$Correct option: D. $5 - x$