Question 446610
{{{1/x + 1/(x+2) = 5/12}}}
<==> {{{(2x+2)/(x(x+2)) = 5/12}}}
<==> {{{12(2x+2) = 5x(x+2)}}}
<==> {{{24x + 24 = 5x^2 + 10x}}}
<==> {{{5x^2 - 14x - 24 = 0}}}
==> (x-4)(5x+6) = 0 ==> x = 4 or -6/5.
Eliminate the second value since it is not an integer.  
Hence the two integers are 4 and 6.