JAMB 1988 · UME · Q12

Simplify $\dfrac{x + 2}{x + 1} - \dfrac{x - 2}{x + 2}$ .

Worked solution (try it first)

Use the common denominator $(x + 1)(x + 2)$ .
The top becomes $(x + 2)^2 - (x - 2)(x + 1)$ .
Expand: $(x + 2)^2 = x^2 + 4x + 4$ and $(x - 2)(x + 1) = x^2 - x - 2$ .
Subtract the whole second product: $x^2 + 4x + 4 - x^2 + x + 2 = 5x + 6$ .
So the answer is $\dfrac{5x + 6}{(x + 1)(x + 2)}$ , option C.