The original expression: $\frac{(x + 2)^{2} - (x + 2) - 20}{x^{2} - 9}$
I was taught to completely factor the numerator and the denominator before stating any non-permissible values, then to cancel out the common factors and simplifying.
So here's what I did:
$\frac{(x + 2)(x + 2) - (x + 2) - 20}{(x - 3)(x + 3)}$
NPV: $x ≠ \pm3$
I cannot simplify it anymore, since there are no common factors.
However, the textbook's answer is $\frac{x + 6}{x + 3}$, while their NPV matches mine.
Did I do something wrong, or is the textbook wrong? I don't understand.
$$\frac{(x + 2)^{2} - (x + 2) - 20}{x^{2} - 9}= \frac{(x + 2-5)(x + 2+4) }{x^{2} - 9} = \frac{(x -3)(x+6)}{(x+3)(x-3)} = \frac{(x+6)}{(x+3)} $$