Question 365787
{{{((x^2+2x-8)/(x^2-16))((x^2-8x+16)/(x^2+3x-10))}}} Start with the given expression.



{{{(((x+4)*(x-2))/(x^2-16))((x^2-8x+16)/(x^2+3x-10))}}} Factor {{{x^2+2x-8}}} to get {{{(x+4)*(x-2)}}}.



{{{(((x+4)*(x-2))/((x-4)*(x+4)))((x^2-8x+16)/(x^2+3x-10))}}} Factor {{{x^2-16}}} to get {{{(x-4)*(x+4)}}}.



{{{(((x+4)*(x-2))/((x-4)*(x+4)))(((x-4)(x-4))/(x^2+3x-10))}}} Factor {{{x^2-8x+16}}} to get {{{(x-4)(x-4)}}}.



{{{(((x+4)*(x-2))/((x-4)*(x+4)))(((x-4)(x-4))/((x+5)*(x-2)))}}} Factor {{{x^2+3x-10}}} to get {{{(x+5)*(x-2)}}}.



{{{((x+4)*(x-2)(x-4)(x-4))/((x-4)*(x+4)(x+5)*(x-2))}}} Combine the fractions. 



{{{(highlight((x+4))highlight((x-2))highlight((x-4))(x-4))/(highlight((x-4))highlight((x+4))(x+5)highlight((x-2)))}}} Highlight the common terms. 



{{{(cross((x+4))cross((x-2))cross((x-4))(x-4))/(cross((x-4))cross((x+4))(x+5)cross((x-2)))}}} Cancel out the common terms. 



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



So {{{((x^2+2x-8)/(x^2-16))((x^2-8x+16)/(x^2+3x-10))}}} simplifies to {{{(x-4)/(x+5)}}}.



In other words, {{{((x^2+2x-8)/(x^2-16))((x^2-8x+16)/(x^2+3x-10))=(x-4)/(x+5)}}}



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