Question 325492


{{{((x^2-81)/(x^2-x-20))/((x^2-8x-9)/(x^2+8x+16))}}} Start with the given expression.



{{{((x^2-81)/(x^2-x-20))((x^2+8x+16)/(x^2-8x-9))}}} Multiply the first fraction {{{(x^2-81)/(x^2-x-20)}}} by the reciprocal of the second fraction {{{(x^2-8x-9)/(x^2+8x+16)}}}.



{{{(((x-9)*(x+9))/(x^2-x-20))((x^2+8x+16)/(x^2-8x-9))}}} Factor {{{x^2-81}}} to get {{{(x-9)*(x+9)}}}.



{{{(((x-9)*(x+9))/((x+4)*(x-5)))((x^2+8x+16)/(x^2-8x-9))}}} Factor {{{x^2-x-20}}} to get {{{(x+4)*(x-5)}}}.



{{{(((x-9)*(x+9))/((x+4)*(x-5)))(((x+4)(x+4))/(x^2-8x-9))}}} Factor {{{x^2+8x+16}}} to get {{{(x+4)(x+4)}}}.



{{{(((x-9)*(x+9))/((x+4)*(x-5)))(((x+4)(x+4))/((x+1)*(x-9)))}}} Factor {{{x^2-8x-9}}} to get {{{(x+1)*(x-9)}}}.



{{{((x-9)*(x+9)(x+4)(x+4))/((x+4)*(x-5)(x+1)*(x-9))}}} Combine the fractions. 



{{{(highlight((x-9))(x+9)highlight((x+4))(x+4))/(highlight((x+4))(x-5)(x+1)highlight((x-9)))}}} Highlight the common terms. 



{{{(cross((x-9))(x+9)cross((x+4))(x+4))/(cross((x+4))(x-5)(x+1)cross((x-9)))}}}  Cancel out the common terms. 



{{{((x+9)(x+4))/((x-5)(x+1))}}} Simplify. 



{{{(x^2+13x+36)/(x^2-4x-5)}}} FOIL. 



So {{{((x^2-81)/(x^2-x-20))/((x^2-8x-9)/(x^2+8x+16))}}} simplifies to {{{(x^2+13x+36)/(x^2-4x-5)}}}.



In other words, {{{((x^2-81)/(x^2-x-20))/((x^2-8x-9)/(x^2+8x+16))=(x^2+13x+36)/(x^2-4x-5)}}}