Question 136138
{{{((n-2)/(n+4))+((n^2+5n+10)/(n+4))}}}


Notice that the denominators are equal.  Therefore you can simply add the numerators directly without having to discover and apply a lowest common denominator.


{{{((n-2)+(n^2+5n+10))/(n+4)}}}


{{{(n^2+6n+8)/(n+4)}}}


Since {{{2*4=8}}} and {{{2+4=6}}}, the numerator trinomial factors to:


{{{(n+2)(n+4)}}}, so the rational expression reduces to:


{{{((n+2)(n+4))/(n+4)}}}.


But {{{(n+4)/(n+4)=1}}}, so eliminate these factors from numerator and denominator leaving you with:


{{{n+2}}}