Simplify the algebraic rational expression: (x^2 - 16) / (x^2 + 7x + 12).
Answer and explanation
Correct answer: D. (x - 4) / (x + 3)
- Step 1: Factor the numerator: x^2 - 16 = (x - 4)(x + 4).
- Step 2: Factor the denominator: x^2 + 7x + 12 = (x + 3)(x + 4).
- Step 3: Cancel the common factor (x + 4) for x != -4: (x - 4) / (x + 3).
Answer
(x - 4) / (x + 3).
Why not the others: Option (x + 4) / (x + 3) cancels (x - 4) instead of (x + 4). Option (x - 4) / (x - 3) incorrectly factors the denominator as (x - 3)(x - 4). Option (x + 4) / (x - 3) has sign errors in both factors.
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