Question 184262


{{{((x^3-1)/(x^2+1))/((9x^2+9x+9)/(x^2-1))}}} Start with the given expression.



{{{((x^3-1)/(x^2+1))((x^2-1)/(9x^2+9x+9))}}} Multiply the first fraction {{{(x^3-1)/(x^2+1)}}} by the reciprocal of the second fraction {{{(9x^2+9x+9)/(x^2-1)}}}.



{{{(((x-1)*(x^2+x+1))/(x^2+1))((x^2-1)/(9x^2+9x+9))}}} Factor {{{x^3-1}}} to get {{{(x-1)*(x^2+x+1)}}}.



{{{(((x-1)*(x^2+x+1))/(x^2+1))(((x-1)*(x+1))/(9x^2+9x+9))}}} Factor {{{x^2-1}}} to get {{{(x-1)*(x+1)}}}.



{{{(((x-1)*(x^2+x+1))/(x^2+1))(((x-1)*(x+1))/(9(x^2+x+1)))}}} Factor {{{9x^2+9x+9}}} to get {{{9(x^2+x+1)}}}.



{{{((x-1)(x^2+x+1)(x-1)(x+1))/(9(x^2+1)(x^2+x+1))}}} Combine the fractions. 



{{{((x-1)highlight((x^2+x+1))(x-1)(x+1))/(9(x^2+1)highlight((x^2+x+1)))}}}  Highlight the common terms. 



{{{((x-1)cross((x^2+x+1))(x-1)(x+1))/(9(x^2+1)cross((x^2+x+1)))}}} Cancel out the common terms. 



{{{((x-1)(x-1)(x+1))/(9(x^2+1))}}} Simplify. 



{{{((x-1)^2(x+1))/(9(x^2+1))}}} Condense the terms.



So {{{((x^3-1)/(x^2+1))/((9x^2+9x+9)/(x^2-1))}}} simplifies to {{{((x-1)^2(x+1))/(9(x^2+1))}}}.