Question 132939
{{{1/a + 1/b = c}}}
multiply both sides by {{{b}}}
{{{b/a + 1 = bc}}}
Subtract {{{bc}}} from both sides
{{{b/a - bc + 1 = 0}}}
Subtract {{{1}}} from both sides
{{{b/a - bc = -1}}}
Factor out {{{b}}} from left side
{{{b(1/a - c) = -1}}}
Divide both sides by {{{1/a - c}}}
{{{b = (-1) / (1/a - c)}}}
To simplify the right side, multiply
the right side by {{{(-a)/(-a)}}}, which is {{{1}}}, 
so nothing is really changed
{{{b = a / (ac - 1)}}} answer
check answer:
{{{1/a + 1/b = c}}}
What is {{{1/b}}}?
{{{1/b = (ac - 1) / a}}} (from the answer)
{{{1/a + (ac-1)/a = c}}}
Multiply both sides by {{{a}}}
{{{1 + ac - 1 = ac}}}
{{{ac = ac}}}
OK