Advanced Math practice question

Answer: A. (x + 2)/(x + 3)

Factor both: x² − x − 6 = (x − 3)(x + 2) and x² − 9 = (x − 3)(x + 3). Cancel the common factor (x − 3): (x + 2)/(x + 3).

Why the other answers are wrong

B. (x − 2)/(x − 3)

The numerator factors as (x − 3)(x + 2), not (x + 3)(x − 2); check the middle term: −3x + 2x = −x.

C. (x + 2)/(x − 3)

The common factor is (x − 3); after cancelling, the denominator keeps (x + 3).

D. (x − 2)/(x + 3)

(x − 2) isn't a factor of x² − x − 6: (x − 2)(x + 3) = x² + x − 6, the wrong middle sign.

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