Answer
$x^{2}-3$
Work Step by Step
Simplifying Rational Expressions
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
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Numerator: factor in pairs
$x^{3}+4x^{2}-3x-12=x^{2}(x+4)-3(x+4)$
$=(x+4)(x^{2}-3)$
Denominator: fully factored.
Expression = $\displaystyle \frac{(x+4)(x^{2}-3)}{(x+4)}$
... divide both with the common factor: $(x+4)$
Expression = $\displaystyle \frac{x^{2}-3}{1}$ = $x^{2}-3$
