Simplify the rational expression: (x^2 - 9) / (2x^2 + 5x - 3).
Answer and explanation
Correct answer: A. (x - 3) / (2x - 1)
- Step 1: Factor numerator difference of squares: x^2 - 9 = (x - 3)(x + 3).
- Step 2: Factor quadratic denominator: 2x^2 + 5x - 3 = (2x - 1)(x + 3).
- Step 3: Cancel common factor (x + 3): [(x - 3)(x + 3)] / [(2x - 1)(x + 3)] = (x - 3) / (2x - 1).
Answer
(x - 3) / (2x - 1).
Why not the others: '(x + 3) / (2x + 1)' cancels wrong terms; '(x - 3) / (2x + 1)' has incorrect sign in denominator; '1 / (2x - 1)' cancels the entire numerator incorrectly.
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