Question 66003
First of all .... thank you for the wonderful grouping.  So many times we have to guess as to what the student is really looking for.
learn this formula/pattern
{{{ (a/b)/(c/d) = ad/bc }}}
{{{ ((x^3+27)/(x+3))/((x^2-3x+9)/(x-3)) }}}
Outsides become the numerator, insides become the denominator
{{{ ((x^3+27)(x-3))/((x^2-3x+9)(x+3)) }}}
Factor the numerator 
{{{ x^3 + 27 = (x+3)(x^2-3x+9) }}}
{{{ ((x+3)(x^2-3x+9)(x-3))/((x^2-3x+9)(x+3)) }}}
Cancel the x+3
{{{ ((x^2-3x+9)(x-3))/(x^2-3x+9) }}}
Cancel the (x^2-3x+9)
{{{ (x-3) }}}