Question 7268
{{{q /( q^2 + 5q + 6)}}}  +  {{{1 / (q^2 + 3q + 2)}}}


{{{q /( q+2)(q+3))}}}  +  {{{1 / (q+1)(q+2)}}}


Make the denominators the same
{{{q /( q+2)(q+3))}}}*{{{(q+1)/(q+1)}}}  +  {{{1 / (q+1)(q+2)}}}*{{{(q+3)/(q+3)}}}


{{{(q)(q+1) /( q+2)(q+3)(q+1)}}}+ {{{(1)(q+3) /( q+2)(q+3)(q+1)}}}


{{{(q^2+q) /( q+2)(q+3)(q+1)}}}+ {{{(q+3) /( q+2)(q+3)(q+1)}}}


{{{(q^2+2q+3) /( q+2)(q+3)(q+1)}}}


{{{(q^2+2q+3)/( q^2+5q+6)(q+1)}}}


{{{(q^2+2q+3)/( q^3+5q^2+6q+6q^2+5q+6)}}}


{{{(q^2+2q+3)/( q^3+11q^2+11q+6)}}}