I got (x-3)(x^2+9) is it right?
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 !
\(\frac{x^5-81x}{x^2+3x}=\\ \frac{x(x^4-81)}{x(x+3)}=\\ \frac{x^4-81}{x+3}=\\ \frac{(x^2-9)(x^2+9)}{x+3}=\\ \frac{(x-3)(x+3)(x^2+9)}{x+3}=\\ (x-3)(x^2+9)\)