The answer is: [tex](f*g)(x)= \frac{3x-9}{x+4}[/tex]
Explanation
Given functions are.......
[tex]f(x)=x^2-7x+12[/tex]
[tex]g(x)= \frac{3}{x^2-16}[/tex]
For finding [tex](f*g)(x)[/tex] , we just need to multiply the two functions [tex]f(x)[/tex] and [tex]g(x)[/tex]. So......
[tex](f*g)(x)= f(x)*g(x)\\ \\ (f*g)(x)= (x^2-7x+12)(\frac{3}{x^2-16})\\ \\ (f*g)(x)= [(x-3)(x-4)][\frac{3}{(x+4)(x-4)}]\\ \\ (f*g)(x)= \frac{3(x-3)}{x+4} = \frac{3x-9}{x+4}[/tex]
