Question 935201
{{{system(x-y=2,xy=24)}}}.
Find {{{1/x+1/y}}}?



{{{1/x+1/y}}}
{{{y/xy+x/xy}}}
{{{(y+x)/(xy)}}}
OR
{{{(x+y)/(xy)}}}
{{{(x+y)/24}}} using one of your given equations.



First equation of the system gives x=y+2.
Substitution gives {{{(y+2)y=24}}}
{{{y^2+2y=24}}}
{{{y^2+2y-24=0}}}
{{{(y-4)(y+6)=0}}}, and according to the restriction given for x and y, must choose {{{highlight_green(y=-6)}}}.  This makes {{{highlight_green(x=-4)}}}.


FINISH THE ANSWER:
{{{(-4-6)/24}}}
{{{-10/24}}}
{{{highlight(-5/12)}}}