Question 145318
{{{((x^2-25)/(x^3-4x^2-5x))((x^2+x)/(1-x^2))}}} Start with the given expression


{{{(((x+5)(x-5))/(x^3-4x^2-5x))((x^2+x)/(1-x^2))}}}   Factor {{{x^2-25}}} to get {{{(x+5)(x-5)}}} 


{{{(((x+5)(x-5))/(x(x-5)(x+1)))((x^2+x)/(1-x^2))}}}   Factor {{{x^3-4x^2-5x}}} to get {{{x(x-5)(x+1)}}} 


{{{(((x+5)(x-5))/(x(x-5)(x+1)))((x(x+1))/(1-x^2))}}}   Factor {{{x^2+x}}} to get {{{x(x+1)}}} 


{{{(((x+5)(x-5))/(x(x-5)(x+1)))((x(x+1))/(-(x+1)(x-1)))}}}   Factor {{{1-x^2}}} to get {{{-(x+1)(x-1)}}} 




{{{((x+5)(x-5)x(x+1))/(-x(x-5)(x+1)(x+1)(x-1))}}} Combine the fractions



{{{((x+5)cross((x-5))cross(x)*cross((x+1)))/(-cross(x)cross((x-5))cross((x+1))(x+1)(x-1))}}} Cancel like terms



{{{-(x+5)/((x+1)(x-1))}}} Simplify



So {{{((x^2-25)/(x^3-4x^2-5x))((x^2+x)/(1-x^2))}}} simplifies to {{{-(x+5)/((x+1)(x-1))}}}