WAEC 2019 · Paper 1 · Q19

Simplify $\dfrac{x^2 - 5x - 14}{x^2 - 9x + 14}$ .

Worked solution (try it first)

Top: two numbers multiplying to $-14$ and adding to $-5$ are $-7$ and $2$ , so $x^2 - 5x - 14 = (x - 7)(x + 2)$ .
Bottom: $-7$ and $-2$ multiply to 14 and add to $-9$ , so $x^2 - 9x + 14 = (x - 7)(x - 2)$ .
Cancel $x - 7$ : $\dfrac{x + 2}{x - 2}$ , option D.