Answer
$\frac{x^2-3x+9}{x-2}, x\ne2, x\ne-3$
Work Step by Step
$\frac{x^3+27}{x^2+x-6}=\frac{(x+3)(x^2-3x+9)}{(x+3)(x-2)}=$$\frac{x^2-3x+9}{x-2}$
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