Numerator: \(x^2 - 9\)
This is a difference of squares, which can be factored as:
\(x^2 - 9 = (x - 3)(x + 3)\)
Denominator: \(x^2 - 4x + 3\)
To factorize this quadratic, we look for two numbers that multiply to 3 and add to -4. These numbers are -1 and -3. Thus,
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