Question 186585


{{{((3)/(a^2+a))((2a+2)/(6))}}} Start with the given expression.



{{{((3)/(a(a+1)))((2a+2)/(6))}}} Factor {{{a^2+a}}} to get {{{a(a+1)}}}.



{{{((3)/(a(a+1)))((2(a+1))/(6))}}} Factor {{{2a+2}}} to get {{{2(a+1)}}}.



{{{((3)/(a(a+1)))((2(a+1))/(2*3))}}} Factor {{{6}}} to get {{{2*3}}}.



{{{(3*2(a+1))/(a*(a+1)(2*3))}}} Combine the fractions. 



{{{(highlight(3)highlight(2)highlight((a+1)))/((a)highlight((a+1))(highlight(2)*highlight(3)))}}} Highlight the common terms. 



{{{(cross(3)cross(2)cross((a+1)))/((a)cross((a+1))(cross(2)*cross(3)))}}} Cancel out the common terms. 



{{{1/a}}} Simplify. 



So {{{((3)/(a^2+a))((2a+2)/(6))}}} simplifies to {{{1/a}}}.



In other words, {{{((3)/(a^2+a))((2a+2)/(6))=1/a}}} where {{{a<>0}}} or {{{a<>-1}}}