Question 220242
Note: {{{f<>0}}} or {{{g<>0}}}



{{{1/f + 1/g}}} Start with the given expression.



{{{g/(fg) + 1/g}}} Multiply the first fraction by {{{g/g}}}



{{{g/(fg) + f/(fg)}}} Multiply the second fraction by {{{f/f}}}



{{{(g+f)/(fg)}}} Combine the fractions.



{{{(fg)/(g+f)}}} Take the reciprocal of the fraction.



Since {{{g+f<>0}}} (to avoid dividing by zero), this means {{{f<>-g}}}.



So the reciprocal of {{{1/f + 1/g}}} is defined whenever {{{f<>-g}}}.