Operations with Functions: (f+g)=f(x)+g(x)?

Question

1. f(x)= x+1/x ; g(x)= x-2/x
2. f(x)= -2/x ; g(x)= x+1/x-3

Please leave an answer with the step-by-step solutions.
thanx. this is the sum of functions.

Answer 1

1) f(x) = x+1/x =(x^2+1)/x
g(x) = x-2/x =(x^2-2)/x
(f+g)(x) = (x^2+x^2+1-2)/x = (2*x^2-1)/x = 2*x -1/x

2) f(x) = -2/x
g(x) = (x+1) / (x-3)
(f+g)(x) = -2/x + (x+1)/(x-3) = {-2*(x-3)+x*(x+1)}/x*(x-3)
= (-2x+6+x^2-x)/(x^2-3x) =(x^2-x+6)/x^2-3x

Answer 2

I`m not sure because I can`t tell whether you mean (x+1)/x or x+(1/x). But, here it goes

1. (x+1)/x + (x-2)/x = (x+1+x-2)/x = (2x-1)/x

if you mean x+(1/x) then it goes like this:

x+(1/x)+x-(2/x)= (x^2 +1+x^2 -2)/x= (2x^2 -1)/x

2. -2/x + (x+1/x-3) = [-2(x-3) + x(x+1)]/(x-3)*x
= [-2x+6 + x^2+x] / x^2 -3x
= [x^2 -x + 6]/ x^2 - 3x

This can`t be simplified.

Answer 3

If by these you mean

1.)
f(x) = (x + 1)/x
g(x) = (x - 2)/x

(f + g)(x) = ((x + 1)/x) + ((x - 2)/x)
(f + g)(x) = ((x + 1) + (x - 2))/x
(f + g)(x) = (x + 1 + x - 2)/x
(f + g)(x) = (2x - 1)/x

ANS : ((2x - 1)/x) or 2 + (1/x)

------------------------------------------------

2.)
f(x) = (-2/x)
g(x) = (x + 1)/(x - 3)

(f + g)(x) = (-2/x) + ((x + 1)/(x - 3))

Multiply everything by x(x - 3)

(f + g)(x) = (-2(x - 3) + x(x + 1))/(x(x - 3))
(f + g)(x) = (-2x + 6 + x^2 + x)/(x(x - 3))
(f + g)(x) = (x^2 - x + 6)/(x^2 - 3x)

if not, then you should had typed them better

Answer 4

Simply add the equations.

1. (f+g)(x) = f(x)+g(x) = (x+1)/x + (x-2)/x = (x+1+x-2)/x

= (2x-1)/x

2. (f+g)(x) = f(x)+g(x) = (-2/x) + (x+1)/(x-3) =

-2(x-3) +x(x+1)
--------------------- =
x(x-3)

x^2-x+6
-----------
x(x-3)

Answer 5

please edit ur question ........make it more clear