<s>[INST] 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.
 [/INST] 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:
$$\frac{x^3+27}{x^2+x-6} = \frac{(x+3)(x^2-3x+9)}{(x+3)(x-2)}=\frac{x^2-3x+9}{x-2}$$
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