Question 144441
{{{((x^3+x^2)/(x^2-16))((x+4)/(3x^4+x^3-2x^2))}}} Start with the given expression


{{{((x^2(x+1))/(x^2-16))((x+4)/(3x^4+x^3-2x^2))}}}   Factor {{{x^3+x^2}}} to get {{{x^2(x+1)}}} 


{{{((x^2(x+1))/((x+4)(x-4)))((x+4)/(3x^4+x^3-2x^2))}}}   Factor {{{x^2-16}}} to get {{{(x+4)(x-4)}}} 


{{{((x^2(x+1))/((x+4)(x-4)))((x+4)/(x^2(x+1)(3x-2)))}}}   Factor {{{3x^4+x^3-2x^2}}} to get {{{x^2(x+1)(3x-2)}}} 



{{{(x^2(x+1)(x+4))/((x+4)(x-4)x^2(x+1)(3x-2))}}} Combine the fractions



{{{(cross(x^2)cross((x+1))cross((x+4)))/(cross((x+4))(x-4)cross(x^2)cross((x+1))(3x-2))}}} Cancel like terms



{{{1/((x-4)(3x-2))}}} Simplify




So {{{((x^3+x^2)/(x^2-16))((x+4)/(3x^4+x^3-2x^2))}}} simplifies to {{{1/((x-4)(3x-2))}}}. In other words, {{{((x^3+x^2)/(x^2-16))((x+4)/(3x^4+x^3-2x^2))=1/((x-4)(3x-2))}}} where {{{x<>-4}}}, {{{x<>-1}}} , or {{{x<>0}}}