Question 11848
{{{1/f=1/s+1/r}}}


Begin by finding the LCD for the entire problem, which is fsr.


Multiply both sides of the equation by fsr:
{{{ (fsr)*(1/f) = (fsr)*(1/s) + (fsr)*( 1/r)}}}


In the first fraction, the f divides out, 
in the second, the s divides out, and
in the third fraction, the r divides out.


What is left will be:

{{{sr = fr + fs}}}


You are solving for s, so get the s terms all on the left side by subtracting fs from each side:
{{{sr - fs = fr + fs - fs}}}

{{{sr - fs = fr}}}


Get the s in one place by factoring out the s:
{{{s(r-f) = fr}}}


Last, divide both sides by (r-f):


{{{ (s*(r-f))/(r-f) = (f*r)/(r-f) }}}


Final answer:
{{{ s = (f*r)/(r-f) }}}


R^2 at SCC