Question 168687


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



{{{(((w-1)(w+1))/(w-1))((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+1)))}}} Factor {{{w^2+2w+1}}} to get {{{(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))(w-1))/(highlight((w-1))highlight((w+1))(w+1))}}} Highlight the common terms. 



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



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



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



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