Question 194479

{{{((x+9)/(x-3))((x^3-27)/(x^2+3x+9))}}} Start with the given expression.



{{{(((x+9))/((x-3)))(((x-3)(x^2+3x+9))/(x^2+3x+9))}}} Factor {{{x^3-27}}} to get {{{(x-3)*(x^2+3*x+9)}}}. Note: use the difference of cubes formula.



{{{((x+9)(x-3)(x^2+3x+9))/((x-3)(x^2+3x+9))}}} Combine the fractions. 



{{{((x+9)highlight((x-3))highlight((x^2+3x+9)))/(highlight((x-3))highlight((x^2+3x+9)))}}} Highlight the common terms. 



{{{((x+9)cross((x-3))cross((x^2+3x+9)))/(cross((x-3))cross((x^2+3x+9)))}}} Cancel out the common terms. 



{{{x+9}}} Simplify. 



So {{{((x+9)/(x-3))((x^3-27)/(x^2+3x+9))}}} simplifies to {{{x+9}}}.



In other words, {{{((x+9)/(x-3))((x^3-27)/(x^2+3x+9))=x+9}}} where {{{x<>3}}}