Question

Consider Functions F and G

Answer 1

A

Explanation:

Answer 2

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.