Question

Consider Functions F and G

Answer 1

Answer:

A

Step-by-step explanation:

We are given two functions:

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

And we want to find:

$f(x)+g(x)$

Thus:

$\displaystyle =\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}$

We can factor the denominator of the first term:

$\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}$

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:

$\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}\Big(\frac{x-4}{x-4}\Big)$

Multiply:

$\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{x-4}{(x+10)(x-4)}$

Combine:

$\displaystyle =\frac{(x-16)+(x-4)}{(x+10)(x-4)}$

Simplify:

$\displaystyle =\frac{2x-20}{(x+10)(x-4)}$

We can expand the denominator:

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

Therefore, our answer is A.

Answer 2

Answer:

A

Step-by-step explanation: