for the question $\displaystyle (x^3-3x^2+4x-12) / (y^2+3)$ i found the answer to be x-3 the book states that there are no restrictions for this question is this right?
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Yes that is right, look at the denominator again: $\displaystyle y^{2} + 3 $. A square term is always greater than or equal to zero. And therefore a square term + a positive number must be greater than zero.
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