Simplify the algebraic fraction completely: (x² - 16) / (2x² + 7x - 4).
Answer and explanation
Correct answer: B. (x - 4) / (2x - 1)
- Step 1: Factor numerator as difference of two squares: x² - 16 = (x - 4)(x + 4). Step 2. Factor denominator: 2x² + 7x - 4 = 2x² + 8x - x - 4 = 2x(x + 4) - 1(x + 4) = (2x - 1)(x + 4). Step 3. Cancel common factor (x + 4): (x - 4) / (2x - 1). Answer: (x - 4) / (2x - 1). Why not the others: (x + 4)/(2x - 1) cancels the wrong factor; sign errors in the other options.
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