Question 706843


{{{((x^2-16)/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))}}} Start with the given expression.



{{{(((x-4)*(x+4))/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))}}} Factor {{{x^2-16}}} to get {{{(x-4)*(x+4)}}}.



{{{(((x-4)*(x+4))/((x+3)*(x+2)))((x^2+5x+4)/(x^2-2x-8))}}} Factor {{{x^2+5x+6}}} to get {{{(x+3)*(x+2)}}}.



{{{(((x-4)*(x+4))/((x+3)*(x+2)))(((x+4)*(x+1))/(x^2-2x-8))}}} Factor {{{x^2+5x+4}}} to get {{{(x+4)*(x+1)}}}.



{{{(((x-4)*(x+4))/((x+3)*(x+2)))(((x+4)*(x+1))/((x+2)*(x-4)))}}} Factor {{{x^2-2x-8}}} to get {{{(x+2)*(x-4)}}}.



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



{{{(highlight((x-4))(x+4)(x+4)(x+1))/((x+3)(x+2)(x+2)highlight((x-4)))}}} Highlight the common terms. 



{{{(cross((x-4))(x+4)(x+4)(x+1))/((x+3)(x+2)(x+2)cross((x-4)))}}} Cancel out the common terms. 



{{{((x+4)(x+4)(x+1))/((x+3)(x+2)(x+2))}}} Simplify. 



So {{{((x^2-16)/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))}}} simplifies to {{{((x+4)(x+4)(x+1))/((x+3)(x+2)(x+2))}}}.



In other words, {{{((x^2-16)/(x^2+5x+6))((x^2+5x+4)/(x^2-2x-8))=((x+4)(x+4)(x+1))/((x+3)(x+2)(x+2))}}}