Question 1171126
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The numbers are n and n+1.


The equation is

    {{{2/n}}} - {{{3/(n+1)}}} = {{{1/2}}}.


Multiply both sides by 2n*(n+1).  You will get

    4(n+1) - 6n = n*(n+1)

    4n + 4 - 6n = n^2 + n

    n^2 + 3n - 4 = 0

    (n-1)*(n+4) = 0.


The roots are  n= 1  and  n= -4.


Both roots work.


<U>ANSWER</U>.  There are two solutions.

         First solution represents numbers 1 and 2.

         Second solution represents numbers -4 and -3.
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Solved.