Given,
[tex]\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12} \\ g(x)=\frac{4x^2-16x+16}{4x+48} \end{gathered}[/tex]
To find the value of f(x) . g(x):
[tex]\begin{gathered} f(x)\times g(x)=\frac{x+12}{x^2+4x-12}\times\frac{4(x^2-4x+4)}{4(x+12)} \\ =\frac{x^2-4x+4}{x^2+4x-12} \\ =\frac{(x-2)(x-2)}{(x-2)(x+6)} \\ =\frac{(x-2)}{(x+6)} \end{gathered}[/tex]
Thus the solution is,
[tex]f(x)\cdot g(x)=\frac{(x-2)}{(x+6)}[/tex]
The answer is option-c
