Question 1048379
Do you need a specific way of dealing with this, or is making a graph acceptable and looking for integer points?


12xy is common denominator.


{{{12xy(1/x+1/y)=12xy(1/12)}}}


{{{12y+12x=xy}}}


{{{xy-12y=12x}}}


{{{y(x-12)=12x}}}


{{{y=(12x)/(x-12)}}}
but does this have a maximum?
{{{dy/dx=((x-12)*12-12x*1)/(x-12)^2}}}, derivative, Quotient Rule.


{{{dy/dx=(12x-144-12x)/(x-12)^2}}}


{{{dy/dx=-144/(x-12)^2}}}------THIS IS NEVER 0.
But you are looking for POSITIVE integers.


You could try positive integers x starting with 0, on {{{y=(12x)/(x-12)}}}.  Would any acceptable y, integer, also be positive?


{{{graph(300,300,-8,8,-8,8,12x/(x-12))}}}


<b>NO.</b>