GCEMathematicsAlgebraic Processes2024

Simplify: $\frac{x^2 - 9}{x^2 - x - 6}$

A$\frac{x - 3}{x - 2}$
B$\frac{x + 3}{x + 2}$
C$\frac{x - 3}{x + 2}$
D$\frac{x + 3}{x - 2}$CORRECT
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Why the answer is D, and why the others tempt you.
The numerator factors as (x+3)(x-3) and the denominator factors as (x-3)(x+2). Cancelling the common factor (x-3) gives (x+3)/(x+2). Wait — that is option B. Re-checking: denominator x²-x-6 = (x-3)(x+2), so the result is (x+3)/(x+2), which is option B.
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