Answer
$f=\frac{p-s}{ps-s} $.
Work Step by Step
The given equation is
$\Rightarrow \frac{1}{s}=f+\frac{1-f}{p}$
Multiply the equation by $p$.
$\Rightarrow p\cdot \left (\frac{1}{s} \right)=p\left (f+\frac{1-f}{p}\right )$
Use the distributive property.
$\Rightarrow \frac{p}{s} =pf+1-f$
Subtract $1$ from both sides.
$\Rightarrow \frac{p}{s}-1 =pf+1-f-1$
Simplify.
$\Rightarrow \frac{p}{s}-1 =pf-f$
Factor out $f$
$\Rightarrow \frac{p-s}{s} =f(p-1)$
Divide both sides by $(p-1)$.
$\Rightarrow \frac{1}{(p-1)}\left (\frac{p-s}{s}\right ) =\frac{f(p-1)}{(p-1)}$
Use the distributive property and simplify.
$\Rightarrow \frac{p-s}{ps-s} =f$
Hence, the solution is $f=\frac{p-s}{ps-s} $.
