Simplify the algebraic fraction (x^2 - 9) / (x^2 + 5x + 6).
Answer and explanation
Correct answer: A. (x - 3) / (x + 2)
- Step 1: Factorise the numerator as a difference of squares: x^2 - 9 = (x - 3)(x + 3). Factorise the denominator: x^2 + 5x + 6 = (x + 2)(x + 3). Step 2. Cancel the common non-zero factor (x + 3) to obtain (x - 3) / (x + 2). Answer: (x - 3) / (x + 2). Why not the others: Cancelling non-factors or inverting signs yields incorrect algebraic forms.
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