Question 168898


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



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



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



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



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



{{{1}}} Simplify. 



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}}} where {{{x<>-3}}}, {{{x<>-2}}}, {{{x<>2}}}, or {{{x<>3}}}