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

## Homework Statement

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

## 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
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
Staff Emeritus
Gold Member
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.

Your answer is correct, there must have been some printing error in the solution.

It seems that the solution manual is incorrect.

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

Mentallic
Homework Helper
Zeion pwned the text book.