Find (f•g) (x) = x^2-7x+12 and g (x) = 3/x^2-16

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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