Question 211596
{{{(1/a) + (1/b) = (1/c)}}}
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Multiply through by {{{(LCD/1)}}} which is {{{(a*b*c/1)}}}

{{{(a*b*c/1)(1/a) + (a*b*c/1)(1/b) = (a*b*c/1)(1/c)}}}

{{{(cross(a)*b*c/1)(1/cross(a)) + (a*cross(b)*c/1)(1/cross(b)) = (a*b*cross(c)/1)(1/cross(c))}}}

{{{b*c + a*c = a*b}}}

Factor out c on the left:

{{{c*(b+a)=a*b}}}

Divide both sides by {{{b+a}}}

{{{c*(b+a)/(b+a)=a*b/(b+a)}}}

{{{c*(cross(b+a))/(cross(b+a))=a*b/(b+a)}}}

{{{c=(ab)/(b+a)}}}

Edwin</pre>