JAMB 1986 · UME · Q29

If $\dfrac ab = \dfrac cd = k$ , find the value of $\dfrac{3a^2 - ac + c^2}{3b^2 - bd + d^2}$ in terms of $k$ .

Worked solution (try it first)

From $\frac ab = \frac cd = k$ , write $a = kb$ and $c = kd$ .
Substitute in the top: $3k^2b^2 - k^2bd + k^2d^2 = k^2(3b^2 - bd + d^2)$ .
The bracket is exactly the bottom, so it cancels and the value is $k^2$ , option D.