Question 117606

{{{((x^2+5x+6)/(x^2-4))((x^2-5x+6)/(x^2-9))}}} Start with the given expression


{{{(((x+3)(x+2))/(x^2-4))((x^2-5x+6)/(x^2-9))}}}   Factor {{{x^2+5x+6}}} to get {{{(x+3)(x+2)}}} 


{{{(((x+3)(x+2))/((x+2)(x-2)))((x^2-5x+6)/(x^2-9))}}}   Factor {{{x^2-4}}} to get {{{(x+2)(x-2)}}} 


{{{(((x+3)(x+2))/((x+2)(x-2)))(((x-3)(x-2))/(x^2-9))}}}   Factor {{{x^2-5x+6}}} to get {{{(x-3)(x-2)}}} 


{{{(((x+3)(x+2))/((x+2)(x-2)))(((x-3)(x-2))/((x+3)(x-3)))}}}   Factor {{{x^2-9}}} to get {{{(x+3)(x-3)}}} 



{{{(x+3)(x+2)(x-3)(x-2)/(x+2)(x-2)(x+3)(x-3)}}} Combine the fractions



{{{cross((x+3))cross((x+2))cross((x-3))cross((x-2))/cross((x+2))cross((x-2))cross((x+3))cross((x-3))}}} Cancel like terms




{{{1}}} Simplify





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Answer:


So {{{((x^2+5x+6)/(x^2-4))((x^2-5x+6)/(x^2-9))}}} simplifies to {{{1}}}. In other words {{{((x^2+5x+6)/(x^2-4))((x^2-5x+6)/(x^2-9))=1}}}