WAEC Mathematics 2016 Paper

Concept:Simplify the algebraic fraction by expanding and factoring both numerator and denominator, then cancelling common factors.Explanation:Start with the given expression:$$\frac{(p-r)^2 - r^2}{2p^2 - 4pr}$$Expand the square in the numerator:$$(p-r)^2 = p^2 - 2pr + r^2$$So the numerator becomes:$$p^2 - 2pr + r^2 - r^2 = p^2 - 2pr$$Factor the numerator:$$p^2 - 2pr = p(p - 2r)$$Factor the denominator:$$2p^2 - 4pr = 2p(p - 2r)$$Now rewrite the whole fraction:$$\frac{p(p - 2r)}{2p(p - 2r)}$$Cancel the common factor $p(p - 2r)$, provided $p \neq 0$ and $p \neq 2r$:$$\frac{1}{2}$$Answer:$$\frac{1}{2}$$ Correct option: A.