given f(x) = x^2 - 7x + 12 and g(x) = 3 / (x^2 - 16)
The product of the two functions, (f•g)(x) is equal to:
(x^2 - 7x + 12) * 3 / (x^2 - 16)
To simplify, factor the two polynomials:
x^2 - 7x + 12 = (x - 4 ) (x - 3 )
x^2 - 16 = (x - 4) (x +4)
=> (f•g)(x) = (x - 4)(x - 3) * 3 / [ (x - 4) (x +4) ] = 3 (x - 3) / (x + 4)
Answer: 3 (x - 3) / (x + 4)
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