Question 253001
{{{ ((x^2+4)/(x^2-4))((x-2)/(x+2)) }}} Start with the given expression.



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



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



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



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



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



{{{(x^2+4)/(x^2+4x+4)}}} FOIL.



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



In other words, {{{((x^2+4)/(x^2-4))((x-2)/(x+2))=(x^2+4)/(x^2+4x+4)}}} where {{{x<>-2}}} or {{{x<>2}}}