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

Based on:

1) g (x) = 3 / (x^2 - 16),

2) f (x) = x^2 - 7x + 12, and

3) (f•g) (x) = the product of the two functions f (x) * g (x)

The solution is found by factoring the two polynomilas f (x) and g (x):

f (x) = x^2 - 7x + 12 = (x - 4) (x - 3)

g (x) = x^2 - 16 = (x - 4) (x + 4)

=> (f•g) (x) = (x - 4) (x - 3) / [ (x - 4) (x + 4) ] = (x - 3) / (x + 4)

Answer: (x - 3) / (x + 4)