Question

The functions f(x) and g(x) are defined below.

Answer 1

Uh im not sure completely but ill try my best to help.

f(x)=x-16/(x+10)(x-4)
g(x)=1/x+10

Now find a common denominator. (x+10)(x-4) is a good one.

x-16/(x+10)(x-4)+x-4/(x+10)(x-4)
2x-20/(x+10)(x-4)

So I think the answer is 2(x-10)/(x+10)(x-4) and x≠-10 and x≠4

Thats the most you can factor it. Don’t try to cancel out the (x-10) and the (x+10)

Brainliest my answer if it helped you out?

Answer 2

Answer:

To find the expression, we have to sum both functions.

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

So,

$f(x) + g(x) = \frac{x-16}{x^{2}+6x-40}+\frac{1}{x+10}\\f(x)+g(x)=\frac{(x-16)(x+10)+(x^{2}+6x-40)}{(x^{2}+6x-40)(x+10)}\\f(x)+g(x)=\frac{(x-16)(x+10)+(x+10)(x-4)}{(x+10)(x-4)(x+10)}\\f(x)+g(x)=\frac{(x-16)+(x-4)}{(x-4)(x+10)}$

Therefore, the sum expression would be:

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