Question

Select the correct answer.

Answer 1

Answer:

Option A

Step-by-step explanation:

Given in the question,

$f(x)=\frac{x-16}{x^2+6x-40}$

$g(x)=\frac{1}{x+10}$

$f(x)+g(x)=\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}$

$=\frac{(x+10)(x-16)+(x^2+6x-40)}{(x+10)(x^2+6x-10)}$

$=\frac{x^2-16x+10x-160+x^2+6x-40}{(x+10)(x^2+6x-40)}$

$=\frac{2x^2-200}{(x+10)(x^2+6x-40)}$

$=\frac{2(x-10)(x+10)}{(x+10)(x^2+6x-40)}$

$=\frac{2(x-10)}{x^2+6x-40}$

$=\frac{2x-20}{x^2+6x-40}$

Therefore, Option A will be the correct option.