Question 371942
{{{N}}} and {{{N+1}}} are the integers.
{{{1/N+1/(N+1)=5/6}}}
Use the common denominator, {{{6N(N+1)}}}
{{{(6(N+1))/(6N(N+1))+(6N)/(6N(N+1))=(5N(N+1))/(6N(N+1))}}}
{{{(6(N+1)+(6N)-5N(N+1))/(6N(N+1))=0}}}
{{{(6N+6+6N-5N^2-5N)/(6N(N+1))=0}}}
{{{(-5N^2+7N+6)/(6N(N+1))=0}}}
Factor the numerator.
{{{((5N+3)(-N+2))/(6N(N+1))=0}}}
Two solutions but only one is an integer solution.
{{{-N+2=0}}}
{{{N=2}}}
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{{{2}}} and {{{3}}} are the integers.