Answer:
[tex]\large\boxed{C.\ \dfrac{2x-20}{x^2+6x-40}}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{x-16}{x^2+6x-40}=\dfrac{x-16}{x+10x-4x-40}=\dfrac{x-16}{x(x+10)-4(x+10)}\\\\f(x)=\dfrac{x-16}{(x-4)(x+10)}\\\\g(x)=\dfrac{1}{x+10}\\\\f(x)+g(x)=\dfrac{x-16}{(x-4)(x+10)}+\dfrac{1}{x+10}=\dfrac{x-16}{(x-4)(x+10)}+\dfrac{1(x-4)}{(x-4)(x+10)}\\\\=\dfrac{x-16+x-4}{(x-4)(x+10)}=\dfrac{2x-20}{(x-4)(x+10)}=\dfrac{2x-20}{x^2+6x-40}[/tex]
