Question 1114940
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Knowing how to solve problems like this using formal algebra is of course valuable....<br>
But logical analysis and a tiny bit of mental arithmetic finds the answer much more quickly.<br>
The reciprocals of integers get very small very quickly.  If the sum of the reciprocals of two integers is 5/12, the integers have to be very small.<br>
Given that the two are consecutive even integers, the solution is found with little effort:
2 and 4? {{{1/2+1/4 = 3/4}}} no...
4 and 6? {{{1/4+1/6 = 3/12+2/12 = 5/12}}} yes!