Question 184586

{{{(x^2-y^2)/(x^2+3xy+2y^2)}}} Start with the given expression.



{{{((x-y)*(x+y))/(x^2+3xy+2y^2)}}} Factor {{{x^2-y^2}}} to get {{{(x-y)*(x+y)}}}.



{{{((x-y)*(x+y))/((x+2y)(x+y))}}} Factor {{{x^2+3xy+2y^2}}} to get {{{(x+2y)(x+y)}}}.



{{{((x-y)highlight((x+y)))/((x+2y)highlight((x+y)))}}} Highlight the common terms. 



{{{((x-y)cross((x+y)))/((x+2y)cross((x+y)))}}} Cancel out the common terms. 



{{{(x-y)/(x+2y)}}} Simplify. 



So {{{(x^2-y^2)/(x^2+3xy+2y^2)}}} simplifies to {{{(x-y)/(x+2y)}}}.



In other words, {{{(x^2-y^2)/(x^2+3xy+2y^2)=(x-y)/(x+2y)}}} where {{{x<>-y}}} or {{{x<>-2y}}}