Consider Functions F and G

Question

asked May 25, 2022 62.0k views

2 Answers

Kerrek SB · Answer 1 · 2022-05-31T02:57:31+0000

Answer:

A

Explanation:

We are given two functions:

$\displaystyle f(x)=(x-16)/(x^2+6x-40)\text{ and } g(x)=(1)/(x+10)$

And we want to find:

f(x)+g(x)

Thus:

$\displaystyle =(x-16)/(x^2+6x-40)+(1)/(x+10)$

We can factor the denominator of the first term:

$\displaystyle =(x-16)/((x+10)(x-4))+(1)/(x+10)$

In order to add the two terms, we must have a common denominator. To achieve this, we can multiply to second term by (x - 4). Therefore:

$\displaystyle =(x-16)/((x+10)(x-4))+(1)/(x+10)\Big((x-4)/(x-4)\Big)$

Multiply:

$\displaystyle =(x-16)/((x+10)(x-4))+(x-4)/((x+10)(x-4))$

Combine:

$\displaystyle =((x-16)+(x-4))/((x+10)(x-4))$

Simplify:

$\displaystyle =(2x-20)/((x+10)(x-4))$

We can expand the denominator:

$\displaystyle =(2x-20)/(x^2+6x-40)$

Therefore, our answer is A.