Verified Answer :

AL2006

Fantastic !  It's not an easy problem.  I'm not even going to go into a
whole big presentation of how to do it.  I'll just simply answer the
question you asked: 

                               Yes! Your answer is correct.

Great work !

konrad509

\(\frac{x^5-81x}{x^2+3x}=\\ \frac{x(x^4-81)}{x(x+3)}=\\ \frac{x^4-81}{x+3}=\\ \frac{(x^2-9)(x^2+9)}{x+3}=\\ \frac{(x-3)(x+3)(x^2+9)}{x+3}=\\ (x-3)(x^2+9)\)

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