Question 187071
I'm going to assume that you meant to write {{{(a^2+2a+1)/(2a^2+3a+1)}}}





{{{(a^2+2a+1)/(2a^2+3a+1)}}} Start with the given expression.



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



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



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



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



{{{(a+1)/(2a+1)}}} Simplify. 



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



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