Question 243102
{{{((x-1)/(x^2+2x+1))((x^2-1)/((x-1)^2))}}} Start with the given expression.



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



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



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



{{{(((x-1))/((x+1)(x+1)))(((x-1)*(x+1))/((x-1)(x-1)))}}} Expand {{{(x-1)^2}}} to get {{{(x-1)(x-1)}}}.



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



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



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



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



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



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