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)

(x - 3) / (x + 4)