Question

Can somebody do this without a calculator please?

Answer 1

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
multiply f to the entire equation
$1= \frac{f}{u}+\frac{f}{v}$
add up right side

$1=\frac{fv}{uv} +\frac{fu}{uv}$
$1= \frac{fv+fu}{uv}$

multiply uv to both sides
$uv= fv+fu$
factor out f
$uv= f(v+u)$
divide (v+u) to both sides
$\frac{uv}{v+u}=f$

substitute in u=3.5cm and v=-4 cm