Question 225117

{{{((w^2-1)/((w-1)^2))((w-1)/(w^2+2w+1))}}} Start with the given expression.



{{{(((w-1)*(w+1))/((w-1)^2))((w-1)/(w^2+2w+1))}}} Factor {{{w^2-1}}} to get {{{(w-1)*(w+1)}}}.



{{{(((w-1)*(w+1))/((w-1)(w-1)))((w-1)/(w^2+2w+1))}}} Break up {{{(w-1)^2}}} to get {{{(w-1)(w-1)}}}.



{{{(((w-1)*(w+1))/((w-1)(w-1)))((w-1)/((w+1)(w+1)))}}} Factor {{{w^2+2w+1}}} to get {{{(w+1)(w+1)}}}.



{{{((w-1)*(w+1)(w-1))/((w-1)(w-1)(w+1)(w+1))}}} Combine the fractions. 



{{{(highlight((w-1))highlight((w+1))highlight((w-1)))/(highlight((w-1))highlight((w-1))highlight((w+1))(w+1))}}} Highlight the common terms. 



{{{(cross((w-1))cross((w+1))cross((w-1)))/(cross((w-1))cross((w-1))cross((w+1))(w+1))}}} Cancel out the common terms. 



{{{1/(w+1)}}} Simplify. 



So {{{((w^2-1)/((w-1)^2))((w-1)/(w^2+2w+1))}}} simplifies to {{{1/(w+1)}}}.



In other words, {{{((w^2-1)/((w-1)^2))((w-1)/(w^2+2w+1))=1/(w+1)}}}