Question 506981

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


{{{((x-1)(x+1)(x+1))/(x^2-2x+1)}}} Use the difference of squares to factor.


{{{((x-1)(x+1)(x+1))/((x-1)(x-1))}}} Factor the denominator.


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


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


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


{{{(x^2+2x+1)/(x-1)}}} FOIL out the numerator.


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


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


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Thanks,


Jim