For what value of x does (1/x) + (1/(1-x)) > 0

[zeion]

Homework Statement

For what value of x does $$\frac{1}{x} + \frac{1}{1-x} > 0$$

Homework Equations

The Attempt at a Solution

So I see that x not = 0 and x not = 1.
Then I added the fractions and see that it will only be positive if the bottom is positive
ie. x(1-x) > 0
I define f(x) = x(1-x) that is a parabola.
It will change signs at x = 0 and x = 1.
So I test some values in the intervals and see that it is positive when 0 < x < 1
So that is the answer.
But the solution says that it is 0 < x < 1 or x > 1?
If I put in 2 > 1 I will get (1/2) + (1/(1-2)) = (1/2)+(1/(-1) = -1/2 not > 0

 

[Hurkyl]

Solution manuals do make mistakes. It sounds like you have a good handle on this proof technique, and have taken advantage of some sanity checks (another would be to graph 1/x + 1/(1-x)) that support your answer and conflict with the manuals, so you would have good reason to remain confident in your solution.

 

[Mandeep Deka]

There's nothing to worry about,
Your answer is correct, there must have been some printing error in the solution.

 

[p21bass]

It seems that the solution manual is incorrect.

edit: began my original response before others posted. Carry on...

 

[Mentallic]

Zeion pwned the textbook.