Question 849203
{{{ 1/a + 1/b  = 1/c }}}
{{{ 1/b = 1/c - 1/a }}}
Multiply both sides by {{{ b }}}
{{{ 1 = b*( 1/c - 1/a ) }}}
divide both sides by  {{{ 1/c - 1/a }}}
{{{ b = 1 / ( 1/c - 1/a ) }}}
Multiply top and bottom of the right side by {{{ a*c }}}
{{{ b = ( a*c ) / ( a - c ) }}}
--------------------------
To check, you can pick any numbers for a, and c.
Then find b
{{{ a = 11 }}}
{{{ c = 7 }}}
------------
{{{ 1/a + 1/b  = 1/c }}}
{{{ 1/11 + 1/b  = 1/7 }}}
{{{ 1/b = 1/7 - 1/11 }}}
{{{ 1/b = .1429 - .0909 }}}
{{{ 1/b = .052 }}}
{{{ b = 19.231 }}}
and
{{{ b = ( a*c ) / ( a - c ) }}}
{{{ b = ( 11*7 ) / ( 11 - 7 ) }}}
{{{ b = 77 / 4 }}}
{{{ b = 19.25 }}}
----------------
I think it's correct, but {{{ 19.231 }}}
and {{{ 19.25 }}} are a little far apart.
{{{ 19.25 }}} should be the right number.
You can recheck.