Simplifying a Rational Expression How do you simplify the following expression:
$$\frac{x^3-27}{x^2+x-6}$$
Thanks for the help. Haven't seen this stuff since high school and I'm trying to help my younger sister out.

The general idea would be to factor, though there aren't any common factors here:
$$\frac{x^3-27}{x^2+x-6} = \frac{(x-3)(x^2+3x+9)}{(x+3)(x-2)}$$
However, if that + in the denominator is the wrong sign, then this can be reduced, assuming $x\neq3$:
$$\frac{x^3-27}{x^2-x-6} = \frac{(x-3)(x^2+3x+9)}{(x-3)(x+2)}=\frac{x^2+3x+9}{x+2}$$
Or one could flip the sign in the numerator for the 27, assume $x\neq-3$ and then:
$$\frac{x^3+27}{x^2+x-6} = \frac{(x+3)(x^2-3x+9)}{(x+3)(x-2)}=\frac{x^2-3x+9}{x-2}$$
