Question 48458
{{{ (1/a)+(1/b)=c }}}
{{{ 1/b = c-(1/a) }}}


And now to get b, we just invert both sides:
{{{ b = 1/(c-(1/a)) }}}


which is not a particular "tidy" answer, so what mathematicians tend to do is this:


from {{{ 1/b = c-(1/a) }}} we re-write the right hand side:
{{{ 1/b = ((ac)/a)-(1/a) }}}
{{{ 1/b = (ac-1)/a }}}


and then we invert:
{{{ b = a/(ac-1) }}}


which is tidier since we don't need the "1/" bit anymore, we just flip the fraction straight away.


I hope this is clear?


jon.