Question

The functions f(x) and g(x) are defined below. Which expression is equal to f(x) + g(x)?

Answer 1

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

Explanation:

Find the complete question attached as a diagram

Given the following

F(x) = x-16/x²+6x-40

Factoring the denominator

F(x) = x-16/x²-4x+10x-40.

F(x) = x-16/x(x-4)+10(x-4)

F(x) = x-16/(x+10)(x-4)

g(x) = 1/x+10

Adding both functions

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

F(x)+g(x) = x-16+(x-4)/(x+10)(x-4)

F(x)+g(x) = x-16+x-4/(x+10)(x-4)

F(x)+g(x) = x+x-16-4/(x+10)(x-4)

F(x)+g(x) = 2x-20/(x+10)(x-4)

F(x)+g(x) = 2(x-10)/(x+10)(x-4)