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Simplify the rational expression by canceling common factors: x²+7x+6/x²−3x−4
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a) x+1/x−4
b) x+2/x−1
c) x+3/x−2
d) x+4​/x−3

Answer :

Final answer:

After factoring the numerator and denominator separately, we find no common factors to cancel between them. Therefore, none of the answer choices provided for the given expression x²+7x+6/x²−3x−4 are correct, indicating a possible error in the question or choices.

Explanation:

To simplify the rational expression x²+7x+6/x²−3x−4, we need to factor both the numerator and the denominator first. The numerator x²+7x+6 can be factored into (x+1)(x+6), and the denominator x²−3x−4 can be factored into (x−1)(x+4). Upon factoring, we get:

(x+1)(x+6)/(x−1)(x+4)

We can cancel common factors that appear in both the numerator and the denominator. However, there are no common factors to cancel, as none of the binomials match. Therefore, none of the answer choices (a, b, c, or d) are correct, which suggests a possible error in the question or the provided choices.

When simplifying expressions, we often look for common factors, and carefully checking the factorization is a crucial step. Once we cancel common factors, we should check the answer to ensure it is reasonable. However, in this case, there was no factor to cancel between the numerator and denominator after factorization.

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