Question 149915

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



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



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





{{{(-(x-y)(x+y)(x+y))/((x+y)(x+y)(x-y))}}} Combine the fractions. 


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



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



{{{-1}}} Simplify. 



So {{{((y^2-x^2)/(x^2+2*x*y+y^2))((x+y)/(x-y))}}} simplifies to {{{-1}}}.