Question 178863

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



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



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



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



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



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



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



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



{{{((x-2)(x-3))/((x+3)(x+2))}}} Simplify. 



{{{(x^2-5x+6)/(x^2+5x+6)}}} FOIL



So {{{((x^2-4)/(x^2+6x+9))((x^2-9)/(x^2+4x+4))}}} simplifies to {{{(x^2-5x+6)/(x^2+5x+6)}}}.



In other words, {{{((x^2-4)/(x^2+6x+9))((x^2-9)/(x^2+4x+4))=(x^2-5x+6)/(x^2+5x+6)}}} where {{{x<>-3}}} or {{{x<>-2}}} (these are the restricted values)