Question 1029589
{{{ 1/x  = 1/r + 1/s }}}
Multiply both sides by {{{ x*r*s }}}
{{{ ( x*r*s )*( 1/x ) = ( x*r*s )*(1/r ) + ( x*r*s )*( 1/s ) }}}
{{{ ( r*s )*( x/x ) = ( x*s )*( r/r ) + ( x*r )*( s/s ) }}}
{{{ ( r*s )*1 = ( x*s )*1 + ( x*r )*1 }}}
Anything times {{{ 1 }}} is the quantity itself,
so you don't need the 1's
{{{ r*s = x*s + x*r }}}
Subtract {{{ x*r }}} from both sides
{{{ r*s - x*r = x*s }}}
Factor out {{{ r }}} on the left side
{{{ r*( s - x ) = x*s }}}
Divide both sides by {{{ s - x }}}
{{{ r = x*s / ( s - x ) }}}
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You can go 1 step further, but it's not necessary
Divide both top and bottom of the right side by {{{ s }}}
{{{ r = x / ( 1 - x/s ) }}}
Hope this helps