Question

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

Which expression is equal to f(x) + g(x)?

Answer 1

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

We know that
`f(x) = (x-16)/(x^(2)+6x-40)` and
`g(x)=(1)/(x+10)`

So,

`f(x) + g(x) = (x-16)/(x^(2)+6x-40)+(1)/(x+10)\\f(x)+g(x)=((x-16)(x+10)+(x^(2)+6x-40))/((x^(2)+6x-40)(x+10))\\f(x)+g(x)=((x-16)(x+10)+(x+10)(x-4))/((x+10)(x-4)(x+10))\\f(x)+g(x)=((x-16)+(x-4))/((x-4)(x+10))`

Therefore, the sum expression would be:

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