JAMB 1997 · UME · Q14

Make $f$ the subject of the formula $t = \sqrt{\dfrac{v}{\frac1f + \frac1g}}$ .

Worked solution (try it first)

Square both sides: $t^2 = \frac{v}{\frac1f + \frac1g}$ , so $\frac1f + \frac1g = \frac{v}{t^2}$ .
Subtract $\frac1g$ : $\frac1f = \frac{v}{t^2} - \frac1g$
$= \frac{gv - t^2}{gt^2}$ .
Turn both sides upside down: $f = \dfrac{gt^2}{gv - t^2}$ , option B.