- #1

zeion

- 466

- 1

## Homework Statement

For what value of x does [tex] \frac{1}{x} + \frac{1}{1-x} > 0 [/tex]

## 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