Question 201443


{{{((x^2+4x-12)/(x^2+4x-32))((x^2+10x+16)/(x^2+10x+24))}}} Start with the given expression.



{{{(((x+6)*(x-2))/(x^2+4x-32))((x^2+10x+16)/(x^2+10x+24))}}} Factor {{{x^2+4x-12}}} to get {{{(x+6)*(x-2)}}}.



{{{(((x+6)*(x-2))/((x+8)*(x-4)))((x^2+10x+16)/(x^2+10x+24))}}} Factor {{{x^2+4x-32}}} to get {{{(x+8)*(x-4)}}}.



{{{(((x+6)*(x-2))/((x+8)*(x-4)))(((x+8)*(x+2))/(x^2+10x+24))}}} Factor {{{x^2+10x+16}}} to get {{{(x+8)*(x+2)}}}.



{{{(((x+6)*(x-2))/((x+8)*(x-4)))(((x+8)*(x+2))/((x+6)*(x+4)))}}} Factor {{{x^2+10x+24}}} to get {{{(x+6)*(x+4)}}}.



{{{((x+6)*(x-2)(x+8)*(x+2))/((x+8)*(x-4)(x+6)*(x+4))}}} Combine the fractions. 



{{{(highlight((x+6))(x-2)highlight((x+8))(x+2))/(highlight((x+8))(x-4)highlight((x+6))(x+4))}}} Highlight the common terms. 



{{{(cross((x+6))(x-2)cross((x+8))(x+2))/(cross((x+8))(x-4)cross((x+6))(x+4))}}} Cancel out the common terms. 



{{{((x-2)(x+2))/((x-4)(x+4))}}} Simplify. 



{{{(x^2-4)/(x^2-16)}}} FOIL



So {{{((x^2+4x-12)/(x^2+4x-32))((x^2+10x+16)/(x^2+10x+24))}}} simplifies to {{{(x^2-4)/(x^2-16)}}}.



In other words, {{{((x^2+4x-12)/(x^2+4x-32))((x^2+10x+16)/(x^2+10x+24))=(x^2-4)/(x^2-16)}}}