NECO 2024 · Paper 1 · Q21

Find $u$ in terms of $f$ and $v$ in the relation $\dfrac1v = \dfrac1f - \dfrac1u$ .

Worked solution (try it first)

Add $\frac1u$ and subtract $\frac1v$ to get $\frac1u$ alone: $\frac1u = \frac1f - \frac1v$ .
Combine over $fv$ : $\frac1u = \frac{v - f}{fv}$ .
Turn both sides upside down: $u = \dfrac{fv}{v - f}$ , option D.