WAEC 2019 · Paper 1 · Q11

If $m : n = 2 : 1$ , evaluate $\dfrac{3m^2 - 2n^2}{m^2 + mn}$ .

Worked solution (try it first)

$m : n = 2 : 1$ , so take $m = 2$ and $n = 1$ (any multiple gives the same value).
Top: $3m^2 - 2n^2 = 3 \times 4 - 2 \times 1$
$= 10$ .
Bottom: $m^2 + mn = 4 + 2 = 6$ .
So the value is $\frac{10}{6} = \frac53$ , option B.