Question 328803
{{{1/n+1/(n+2)=12/35}}}
Multiply both sides by {{{35n(n+2)}}}
{{{35(n+2)+35n=12n(n+2)}}}
{{{35n+70+35n=12n^2+24n}}}
{{{12n^2-46n-70=0}}}
{{{6n^2-23n-35=0}}}
{{{(6n+7)(n-5)=0}}}
Only one of the factors will provide an integer solution.
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{{{n-5=0}}}
{{{highlight(n=5)}}}
The two integers are 5 and 7.
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Verified,
{{{1/5+1/7=7/35+5/35=12/35}}}}