The simplified form of the rational expression (x²+x-12)/(x²+9x+20) is (x-3)/(x+5) after factoring the numerator and denominator and canceling out the common factor.
The given rational expression is (x²+x-12)/(x²+9x+20). In order to simplify this, we need to factor both the numerator and the denominator. The factored form of the numerator (x²+x-12) is (x-3)(x+4) and the factored form of the denominator (x²+9x+20) is (x+4)(x+5).
After factoring, the expression becomes (x-3)(x+4) / (x+4)(x+5), simplifying this we can cancel out the common factor (x+4) from the numerator and the denominator. Hence, the simplified form of the given rational expression is (x-3) / (x+5).
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